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.

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

28. Blood Types The probability that a Latinx American person in the United States has type A+ blood is 29%. Four Latinx American people in the United States are selected at random. (Source: American National Red Cross)

b. Find the probability that none of the four have type A+ blood.

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).

33. P(A) = 2/3, P(A') = 1/3, P(B|A) = 1/5 , and P(B|A') = 1/2

3. What does the notation P(B|A) mean?

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).

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%