Tree Diagrams and Conditional Probability

Section 11 - 4: Conditional Probability

GOAL: To be able to find conditional probability using tables and/or tree diagrams.

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Probability Review #1: What is the sample space (total number of outcomes) when you flip a coin four times? The total number of outcomes is

.

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Probability Review #2: What is the probability of flipping a coin 4 times and flipping the same side all four times. This is four heads OR four tails. Leave your solution as a decimal.

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Probability Review #3: A basketball player attempted 24 shots and made 13 in their last game. How many shots can you expect the player to make if they attempt 15 shots?

Multiple Choice

The table is the results of a survey about favorite sport to watch on TV. What is the probability that a person chosen at random would prefer football given they are a female.

• 2/25

• 3/13

• 12/73

• 26/75

Conditional Probability

The probability that an event, B, will occur given that another event, A, has already occurred. For the previous question; given they are a female...how many females? This is the "out of." Of those females how many prefer football?

Let's try it...

• Probability of randomly selecting a person who is a male given they prefer baseball?

• Prefer Baseball (the "out of") = 60. Males who prefer baseball (what you want) = 15.

• The probability would be 1/4 or .25 or 25%

Multiple Choice

Chelsea surveyed a sample of students in the senior class to determine the distribution of students with a drivers' license. The results are in the table. What is the probability of selecting a student at random that is a female?

• 1/2

• 11/20

• 1/4

• 11/40

Multiple Choice

Find the probability that a person selected at random is a male given they have no license.

• 1/2

• 5/8

• 3/4

• 1/3

Multiple Choice

Find the probability that a student chosen at random has a Learner's Permit given they are a female.

• 5/8

• 1/2

• 1/4

• 3/5

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Assuming the poll is representative of all eligible voters, find the probability that a person voted in the last presidential election given that they had a degree. The probability is

%

Break down the Chart Further

• College Degree of No College Degree

• Voted or Did Not Vote

• With conditional probability you simply follow the branches.

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Find the probability that a voter selected at random went to college but did not vote.

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Find the probability that a person selected at random did not vote in the last election.

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Practice this idea: You will need to draw a tree here.

A survey was conducted amongst students about being right - or left - handed. Of those that responded, 17% identified as male. Of the those, 33% were left - handed. 90% of the female identifying respondents were right - handed. What is the probability that a female identifying respondent is left - handed?

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Practice this idea: You will need to draw a tree here.

Same survey; 17% identify as male, 33% of those identify as left - handed. 90% of the female identifying respondents were right - handed. If 200 people responded, how many were right - handed males?