Twelve people are applicants for a job. Nine of the applicants are competent for

Question

Twelve people are applicants for a job. Nine of the applicants are competent for the job; Three are not competent. Two should be hired
A) How many different pairs of people are possible? How many couples is there one or both are competent? If two are chosen randomly among the twelve, what is the probability that nobody is competent? Twelve people are applicants for a job. Nine of the applicants are competent for the job; Three are not competent. Two should be hired
A) How many different pairs of people are possible? How many couples is there one or both are competent? If two are chosen randomly among the twelve, what is the probability that nobody is competent? Twelve people are applicants for a job. Nine of the applicants are competent for the job; Three are not competent. Two should be hired
A) How many different pairs of people are possible? How many couples is there one or both are competent? If two are chosen randomly among the twelve, what is the probability that nobody is competent?

Explanation / Answer

Total people = 12

Number of competent = 9

Number of non competent = 3

A) Number of different pairs of people are possible = 12C2 = 12!/(2!*10!) = 66

Number of pairs with one or both are competent = total - number of pairs with no competent = 66 - 3C2 = 66 - 3 = 63

P(none of them are competent) = 3C2 / 12C2 = 3 / 66 = 0.045

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