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.)

Bachelor's Master's Professional Doctorate Female 932 403 52 28 Male 663 270 42 28

Explanation / Answer

a) Probability that a randomly chosen degree recipient is a man

P(man) = (Total degrees earned by male)/(Total earned degrees) = 1003/2418 = 0.4148

b) What is the conditional probability that the person chosen received a bachelor's degree, given that he is a man = P(A|B)

where A is a person having Bachelor's Degree

B That person should be a Man

P(A|B) = 663/1003 = 0.6610

c) Using Multiplicative rule choosing a male bachelors degree reciepent

= P(man)*P(bahelors degree given Male)

= (1003/2418)*(663/1003) = 0.2742

Using table of counts probability of male bachelors degree reciepent

P(Male bachelors degree reciepent) = total male bachelor degrees / total degrees

                                                    = 663/2418 = 0.2742

Bachelor's Master's Professional Doctorate Total Female 932 403 52 28 1415 Male 663 270 42 28 1003 Total 1595 673 94 56 2418

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