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Conditional Probability

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Finding Conditional Probability Definition 1: A conditional probability contains a condition that may limit the sample space for an event. You can write a conditional probability using the notation P(B | A), read “the probability of event B, given event A.”

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Example 1 The table shows the results of a class survey. A. Find P(did a chore | male). B. Find P(female | did a chore).

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Example 2 Recycle Americans recycle increasingly more materials through municipal waste collection each year. The table shows recycling data for a recent year. Find the probability that a sample of recycled waste was paper. Find the probability that a sample of recycled waste was paper. Find the probability that a sample of recycled waste was plastic.

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Using Formulas and Tree Diagrams Property: Conditional Probability Formula: For any two events A and B from a sample space with P(A) ≠ 0.

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Example 3 Market Research Researchers asked shampoo users whether they apply shampoo directly to the head, or indirectly using a hand. Find the probability that a respondent applies shampoo directly to the head, given that the respondent is female. P(directly to head|female) =

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Ticket Out the Door The table below shows the results of a class survey. Do You Own a Pet? 1. Find P(own a pet|female). 2. Find P(male|don’t own a pet). YesNo Female86 Male57

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Tree Diagrams

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Example 4 A student in Buffalo, New York, made the observations below. Of all snowfalls, 5% are heavy (at least 6 in.). After a heavy snowfall, schools are closed 67% of the time. After a light (less than 6 in.) snowfall, schools are closed 3% of the time. Find the probability that the snowfall is light and the schools are open. Make a tree diagram. Use H for heavy snowfall, L for light snowfall, C for schools closed, and O for schools open.

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Example 4 Continued a. Find P(L and O) b. Find P(Schools open, given heavy snow)

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Example 5 Make a tree diagram based on the survey results below. Then find P(a female respondent is left-handed) and P(a respondent is both male and right-handed). Of all the respondents, 17% are male. Of the male respondents, 33% are left-handed. Of female respondents, 90% are right-handed. P(female is left-handed) = P(both male and right-handed) =

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Ticket Out the Door A student made the following observations of the weather in his hometown. On 28% of the days, the sky is mostly clear. During the mostly clear days, it rained 4% of the time. During the cloudy days, it rained 31% of the time. Use a tree diagram to find the probability that a day will start out clear, and then it will rain.

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11.4 CONDITIONAL PROBABILITY Learning Goal find conditional probabilities use table and tree diagrams to determine conditional probabilities.

11.4 CONDITIONAL PROBABILITY Learning Goal find conditional probabilities use table and tree diagrams to determine conditional probabilities.

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