4. Probability

True or False? In Exercises 5 and 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

6. If events A and B are dependent, then P(A and B) = P(A) · P(B).

Finding Conditional Probabilities In Exercises 7 and 8, use the table to find each conditional probability.

8. Retirement Savings The table shows the results of a survey in which 250 male and 250 female workers ages 25 to 64 were asked if they contribute to a retirement savings plan at

work.

b. Find the probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work.

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

14. A ball is selected from a bin of balls numbered from 1 through 52. It is replaced, and then a second numbered ball is selected from the bin.

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.

17. A study found that there is no relationship between playing violent video games and aggressive or bullying behavior in teenagers. (Source: The Royal Society Publishing)

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

20. Coin and Die A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.

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%

In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.

19. Tossing a coin four times and getting four heads, and then tossing it a fifth time and getting a head

Manufacturing An assembly line produces 10,000 automobile parts. Twenty percent of the parts are defective. An inspector randomly selects 10 of the parts

b. Because the sample is only 0.1% of the population, treat the events as independent and use the binomial probability formula to approximate the probability that none of the selected parts are defective.

Finding New Music In Exercises 45–48, use the pie chart, which shows the results of a survey of 513 music listeners who were asked about their primary source for new music. (Source: The Sound of AI)

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47. You choose nine music listeners at random. What is the probability that none of them say their primary source for new music is friends or social media?

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

27. Blood Types The probability that a person of Asian descent in the United States has type O+ blood is 39%. At random, six people of Asian descent in the United States are selected. (Source: American National Red Cross)

c. Find the probability that at least one of the six has type O+ blood.