probability and statistics

Question

A club has 21 members, four of whom are executives. Five members are randomly selected to take part in a survey.



a) What is the probability that four non-executive members are chosen?

b) what is the expected number of non executive members?

Answer 1

You have 17 non-executives out of 21 members.

You want to find the probability that in a sample of 5 you will pick 4 non-executives

we are dealing with a hypergeometric distribution experiment

probability =

ways to pick 4 non-executives out of 17 * ways to pick 1 executive out of 4

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ways to pick 5 out of 21

C(17,4)*C(4,1)

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C(21,5)

expected number of non-executives is 5 * 17 /21 = 4.05