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Section 12.2

Section 12.2 . Conditional Probability. Finding Conditional Probability.

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Section 12.2

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  1. Section 12.2 Conditional Probability

  2. 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.”

  3. 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).

  4. 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.

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

  6. 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) =

  7. 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).

  8. Tree Diagrams

  9. 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.

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

  11. 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) =

  12. 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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