Boy or Girl? In Exercises 71-74, a couple plans to have three children. Each child is equally likely to be a boy or a girl.
71. What is the probability that all three children are girls?

Using a Pie Chart to Find Probabilities In Exercises 83-86, use the pie chart at the left, which shows the number of workers (in millions) by occupation for the United States. (Source: U.S. Bureau of Labor Statistics)

84. Find the probability that a worker chosen at random is not employed in a service occupation.

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34. Lottery Number Selection A lottery has 52 numbers. In how many different ways can six of the numbers be selected? (Assume the order of selection is not important.)

"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.

13. Rolling a six-sided die and then rolling the die a second time so that the sum of the two rolls is five"

"Classifying Events Based on Studies In Exercises 15-18, identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.

16. A study found no significant association between the use of talc powder and the incidence of ovarian cancer in women. (Source: JAMA)"

According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is

P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').

In Exercises 33–38, use Bayes’ Theorem to find P(A|B).

37. P(A) = 73%, P(A') = 17%, P(B|A) = 46% , and P(B|A') = 52%

20. Skating Eight people compete in a short track speed skating race. Assuming that there are no ties, in how many different orders can the skaters finish?