Transcript Probability - Iroquois Central School District / Home Page

Probability
Tree Diagram: A diagram with branches
that is used to list all possible outcomes.
Example: Meal choices: Burger, hot dog, Pizza
Drinks: coke or sprite
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Sample space: A list of all the possible
outcomes.
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Example: The sample space for rolling a dice is
{1, 2, 3, 4, 5, 6}.
Counting Principle: a way to find the
number of possible outcomes of an event.
**Just multiply the number of ways each activity
can occur.
Try the following
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Andy flips a coin and spins a spinner with 3 equal
sections marked A, B, C. a) Draw a tree diagram,
b) What is the sample space (i.e. all possible
outcomes)? How many outcomes are in the sample
space?
HA
HB
HC
TA
TB
TC
6 outcomes
For the lunch special at Nick’s Deli, customers can
create their own sandwich by selecting 1 type of
bread and 1 type of meat from the selection below.
c
a) In the space below, list all the possible sandwich
combinations using 1 type of bread and 1 type of
meat.
WC
RC
WRb RRb
b) If Nick decides to add whole wheat bread as
another option, how many possible sandwich
combinations will there be?
6 outcomes
Helen is preparing candy bags for the children at a
party. She has 2 flavors of lollipops, 4 types of
candy bars, and 6 flavors of chewy candies. If each
bag contains one piece of each type of candy, what
is the total number of possible candy combinations
for the bags?
A) 12
B) 15
C) 36
D) 48
Peter has 6 sweatshirts, 4 pairs of jeans, and 3
pairs of shoes. How many different outfits can
Peter make using one sweatshirt, one pair of jeans,
and one pair of shoes?
A) 13
B) 36
C) 72
D) 144
Erin wants to make a sandwich from the main
ingredients shown in the table below.
In the space below, list all the possible ways Erin
can make a sandwich using one type of bread and
one main ingredient.
SP
SH ST
SE
WP WH WT WE
RP RH RT RE
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Probability: is the likelihood that an
event will occur.
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Probability of getting a tail when tossing a coin
Experiment: an activity involving chance,
such as rolling a cube
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Tossing a coin is the experiment
Trial: Each repetition or observation of an
experiment
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Each time you toss the coin is a trial
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Outcome: A possible result of an event.
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Event: A set of one or more outcomes
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Example: Heads or tails are possible outcomes
when tossing a coin
Example: Getting a heads when you toss the coin
is the event
Compliment of an Event: The outcomes
that are not the event

Example: Probability of rolling a 4 = 1/6. Not
rolling a 4 = 5/6.
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Probability is always between 0 and 1.
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Probability = 0 means that the event will
NEVER happen.
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Example: The probability that the Bills will win the
Super Bowl this year.
Probability = 1 means the event will
ALWAYS happen.
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Example: The probability that Christmas will be on
December 25th next year.
_______________
_______________
____________
___
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Rolling a 0 on a number cube
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Rolling a number less than 3 on a number cube
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Equally likely
Rolling a number greater than 2 on a dice
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Unlikely
Rolling an even number on a number cube
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Impossible
Likely
Rolling a number less than 7 on a number cube
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Certain
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Experimental Probability: is based on an
experiment. The probability of what
ACTUALLY did happened.
Try the following
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Example 1: During football practice, Sam made 12
out of 15 field goals. What is the probability he will
make the field goal on the next attempt?3
12/15
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Example 2: Ms. Sekuterski’s student have taken
out 85 books from the library. 35 of them were
fiction. What is the probability that the next book
checked out will be a fiction book?
35/38
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Example 3: Emma made 9 out of 15 foul shots
during the first 3 quarters of her basketball game.
What is the probability that the next time she takes
a foul shot she will make it?
9/15
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Example 4: Christina scored an A on 7 out of 10
tests. What is the probability she will score an A on
her next test?
7/10
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Theoretical Probability: the probability of
what should happen. It’s based on a rule:
# of favorable outcomes
# of possible outcomes
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Example: Rolling a dice and getting a 3 =
1
6
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Example 1: Andy has 10 marbles in a bag. 6 are
white and 4 are blue. Find the probability as a
fraction, decimal, and percent of each of the
following:
a) P(blue marble)
4/10
b) P(white marble)
6/10
Example 2: If there are 12 boys and 13 girls in
a class, what is the probability that a girl will be
picked to write on the board?
13/25
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Example 3: There are 8 black chips in a bag of
30 chips. What is the probability of picking a black
chip from the bag?
8/30
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Example 4: There are 2 small, 5 medium, and 3
large dogs in a yard. What is the probability that
the first dog to come in the door is small?
2/10
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Example 5: What is the probability of getting a
tail when flipping a coin?
1/2
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Example 6:
on a die?
1/6
What is the probability of rolling a 4
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Independent: the outcome of one
event DOESN’T effect the probability
of another event

Example: Find the probability of choosing a
green marble at random from a bag
containing 5 green and 10 white marbles
and then flipping a coin and getting tails.
5/15 x ½ = 5/30 = 1/6
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Replacement: DOESN’T effect the
probability of another event
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Example: A drawer contains 3 red
paperclips, 4 green paperclips, and 5 blue
paperclips. One paperclip is taken from
the drawer and then replaced. Another
paperclip is taken from the drawer. What
is the probability that the first paperclip is
red and the second paperclip is blue?
3/12 x 5/12 = 15/144 = 5/48
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Dependent: the outcome of one event
DOES effect the probability of another
event
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Example: Micah has five $1 bills, three
$10 bills, and two $20 bills in her wallet.
She picks two bills at random. What is
the probability of her picking the two $20
bills?
2/10 x 1/9 = 2/90 = 1/45
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Without Replacement: DOES effect
the probability of another event
Example: A bag contains 3 blue and 5 red
marbles. Find the probability of drawing 2 blue
marbles in a row without replacing the first
marble.
3/8 x 2/7 = 6/56 = 3/28
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OR Probabilities: Add the probabilities
Example: Rolling either a 5 or a 6 on a 1 – 6
number cube.
P(5 or 6)
1/6 + 1/6 = 2/6 = 1/3
Example 2: Choosing either an A or an E from
the letters in the word mathematics.
P(A or E)
2/11 + 1/11 = 3/11
1. Spinning red or green on a spinner that has 4
sections (1 red, 1green, 1 blue, 1 yellow)
¼ + ¼ = 2/4 = ½
2. Drawing a black marble or a red marble from a
bag that contains 4 white, 3 black, and 2 red
marbles.
3/9 + 2/9 = 5/9
3. Choosing either a number less than 3 or a
number greater than 12 from a set of cards
numbered 1 – 20.
2/20 + 8/20 = 10/20 = ½

AND Probabilities: Multiply the
probabilities
Example 1:
A die is rolled. What is the
probability that the number rolled is greater than 2
and even?
P( >2 and Even)
Example 2: From a standard deck of cards, one card
is drawn. What is the probability that the card is black
and a jack?