19. 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.

B Apply

20. Suppose A and B are independent events, with P(A) = 0.60 and P(B) = 0.25. Find each probability.
    1. P(A and B)
    2. P(A | B)
    3. What do you notice about P(A) and P(A | B)?
    4. Reasoning One way to describe A and B as independent events is The occurrence of B has no effect on the probability of A. Explain how the answer to part (c) illustrates this relationship.
21. Think About a Plan A math teacher gives her class two tests. 60% of the class passes both tests and 80% of the class passes the first test. What percent of those who pass the first test also pass the second test?
    • What conditional probability are you looking for?
    • How can a tree diagram help you solve this problem?

Weather Use probability notation to describe the chance of each event. Let S, C, W, and R represent sunny, cloudy, windy, and rainy weather, respectively.

22. cloudy weather
23. sunny and windy weather
24. rainy weather if it is windy
25. Transportation You can take Bus 65 or Bus 79. You take the first bus that arrives. The probability that Bus 65 arrives first is 75%. There is a 40% chance that Bus 65 picks up passengers along the way. There is a 60% chance that Bus 79 picks up passengers. Your bus picked up passengers. What is the probability that it was Bus 65?

The tree diagram relates snowfall and school closings. Find each probability. Let H, L, O, and C represent heavy snowfall, light snowfall, schools open, and schools closed, respectively.

26. P(C)
27. P(H and O)
28. P(H | C)
29. P(L | O)
30. P(L | C)
31. P(H | O)

Image Long Description

C Challenge

32. 1. Writing Explain which branches of the tree diagram below represent conditional probabilities. Give a specific example.
    2. Are the event of having a license and the event of being an adult independent events? Justify your answer.
    3. Open-Ended Estimate probabilities for each branch of the tree diagram for your city or town. Then find P(L).

    
    Image Long Description

    A = adult (21 or older)

    M = minor (under 21)

    L = licensed driver

    N = not licensed to drive

33. Reasoning Sixty percent of a company's sales representatives have completed training seminars. Of these, 80% have had increased sales. Overall, 56% of the representatives (whether trained or not) have had increased sales. Use a tree diagram to find the probability of increased sales, given that a representative has not been trained.

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