There are 78 qualified applicants for teaching positions in an elementary school

Question

There are 78 qualified applicants for teaching positions in an elementary school, of which some have at least five years' teaching experience and some have not, some are married and some are single, with the exact breakdown being The order in which the applicants are interviewed is random. M is the event that the first applicant interviewed is married and F is the event that the first applicant interviewed has at least five years teaching experience. Find the following probabilities: Pr[M], Pr[F], Pr[MAF], Pr[M|F], Pr[F|M], Are M and F independent? Suppose that there is only one opening in the third grade, and each applicant with at least five year experience has twice the chance of an applicant with less than five year experience. Let U denote the event that the job goes to one of the single applicants, and V the event that it goes to an applicant with less than five year experience. Find the following probabilities: Pr[U], Pr[V], Pr[U Lambda V], Pr[U|V], Pr[V|U]. Are U and V independent?

Explanation / Answer

prob (M) = 48/78 =0.61

pr(F) = 30/78 = 0.38

p(M^F) = 18/78 = 0.23

p(M|F) = 0.23/0.38 =0.61

p(F|M) = 0.23/0.61=0.38

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