Here are the projected numbers (in thousands) of earned degrees in a certain cou

Question

Here are the projected numbers (in thousands) of earned degrees in a certain country during one academic year, classified by level and by the sex of the degree recipient:

Use these data to answer the following questions.

(a) What is the probability that a randomly chosen degree recipient is a man? (Round your answer to four decimal places.)


(b) What is the conditional probability that the person chosen received a bachelor's degree, given that he is a man? (Round your answer to four decimal places.)


(c) Use the multiplication rule to find the probability of choosing a male bachelor's degree recipient. Check your result by finding this probability directly from the table of counts. (Round your answer to four decimal places.)

Explanation / Answer

Total people = 935 + 403 + 52 + 28 + 664 + 270 + 45 + 28 = 2425

a) P(man) = (664 + 270 + 45 + 28) / 2425

                = 1007 / 2425

                = 0.4153

b) P(bachelor's degree | man) = P(bachelor's degree and man) / P(man)

                                                = (664 / 2425) / (1007 / 2425)

                                                = 664 / 1007

                                                = 0.6594

c) P(male bachelor's degree) = P(bachelor's degree | man) * P(man)

                                               = 0.6594 * 0.4153

                                               = 0.2738

P(male bachelor's degree) = 664 / 2425 = 0.2738

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