Transcript Probability - Mukwonago Area School District

Probability
COMPOUND EVENTS
If two sets or events have no elements in common, they are called
disjoint or mutually exclusive.
Examples of mutually exclusive sets:
Two fair dice are tossed, what is the probability of a sum of 7 or 11?
A card is randomly selected from a standard deck of cards.
What is the probability that it is a 10
If A and B are
OR
a face card?
disjoint events, then the probability of A OR B is:
P( A or B) = P(A ) + P(B)
Examples of mutually exclusive sets:
Two fair dice are tossed, what is the probability of a sum of 7 or 11?
:
P( A or B) = P(7 ) + P(11)
6
2
= +
36
=
8
36
36
Examples of mutually exclusive sets:
A card is randomly selected from a standard deck of cards.
What is the probability that it is a 10
OR
a face card?
:
P( A or B) = P(10 ) + P(F)
4
12
= +
52
52
16
4
= =
52 13
Examples of mutually exclusive sets:
In this last situation there is no overlap:
10
10
10
10
But if I changed the question to:
A card is randomly selected from a standard deck of cards.
What is the probability that it is a 10
OR
a heart?
So we need to modify our formula and subtract out
that overlap so we don’t count it twice:
:
P( A or B) = P(10 ) + P(
=
4
13
+
52
52
=
)-P(10 and )
-
1
52
16
52
This is called a COMPOUND EVENT .
Two sets are INDEPENDENT if the occurrence of
one has NO EFFECT on the occurrence of the other.
Examples of independent:
Two fair dice are tossed, what is the probability of a sum
of 12?
A computer generates three random numbers….
P( A and B) = P(A ) ∙ P(B)
NOTICE: There is no “ or”.
Compound events ask for probability of this
“ or” that . If there is overlap we are also
able to find a this “and” that”.
12
3
𝑃 𝐴 𝑎𝑛𝑑 𝐵 =
=
200 50
Out of 200 students 113 are either varsity athletes or on
the honor roll. There are 74 students who are varsity
athletes and 51 who are on the honor roll. What is the
probability that a randomly selected senior is both a
varsity athlete AND on the honor roll?
:
P( A or B) = P(A ) + P(B)-P(A and B )
113
200
=
74
200
+
51
200
- P(A and B)
Rewrite as:
𝑃(𝐴 𝑎𝑛𝑑 𝐵) =
74
51
+
200
200
-
113
200