Transcript 11.4 Notesx - Rachel Holtkamp Math
Slide 1
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 2
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 3
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 4
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 5
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 6
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 7
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 8
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 2
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 3
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 4
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 5
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 6
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 7
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524
Slide 8
11.4 – Compound Events
A simple event is an event that describes a
single outcome.
A compound event is an event made up of
two or more simple events.
Mutually exclusive events are events that
cannot both occur in the same trial of an
experiment.
Union
Probability of Mutual
Exclusive Events
means
If A and B are mutually exclusive events, then
“or”
P A B P A P B
A group of students is donating blood during a
blood drive. A student has a 9/20 probability
of having type O blood and a 2/5 probability
of having type A blood.
A.
Why are the events “type O” and “type A” blood mutually
exclusive?
You can’t have type A and type O at the same time
B. What is the probability that a student has type O or type A
blood?
9/20 + 2/5 = 17/20
Inclusive events are events that have one or
more outcomes in common.
Probability of Inclusive Events
If A and B are inclusive events, then
P A B P A P B P A B
Intersection
means
“and”
Find each probability on a number cube.
A. Rolling a 4 or an even number
P(4) = 1/6
P(even) = ½
A 4 is an even number, so the
Probability of the intersection is 1/6
P(4 or an even number) = 1/6 + ½ - 1/6 = ½
B. Rolling an odd number or a number greater than
2
3/6 + 4/6 – 2/6 = 5/6
1
5
3
6
4
Of 1560 juniors and seniors surveyed, 840
were seniors and 630 read a daily paper.
Only 215 of the paper readers were
juniors. What is the probability that a
student was senior or read a daily paper?
1055
840
630
415
1560
1560
1560
1560
67 . 6 %
425
215
415
840
630
seniors
Paper
readers
Each of 6 students randomly chooses a butterfly
from a list of 8 types. What is the probability that at
least 2 students choose the same butterfly?
Use the complement!!!
What’s the probability that 2 students choose the same butterfly?
What’s the probability that 3 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)
What’s the probability that 4 students choose the same butterfly?
P(all choose
different)
= numberthat
of ways
6 students
choose
different
butterflies
What’s
the probability
5 students
choose
the same
butterfly?
total number
ways 6choose
students
can
choose
butterflies .
What’s the probability
that 6 of
students
the
same
butterfly?
8
P6
8
6
87 6 54 3
8 8 8 8 8 8
20160
0 . 0769
262144
P(at least 2 students choose same) = 1 – P(all choose different)
= 1 – 0.0769 ≈ 0.9231
.
In one day, 5 different customers bought
earrings from the same jewelry store. The store
offers 62 different styles. Find the probability
that at least 2 customers bought the same style.
About .1524