There are 78 qualified applicants for teaching positions in an elementary school
ID: 3203650 • Letter: T
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 (a) 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[M F], Pr[M|F], Pr[F|M]. Are M and F independent? (b) 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 V], Pr[U|V], Pr[V|U]. Are U and V independent?Explanation / Answer
a) Pr(m)= probability of married applicant = number of married applicant/total number of applicants
=18+30 / 78 = 48/78 = 0.61533
SImilarly Pr(F)= probability of applicant with 5 years of experience
= number of applicant with 5 years of experience / total number of applicants = 18+12 / 78 = 30/78= 0.3846
Pr(M / F) = Number of married applicants with 5 years of experience/total number of applicants = 18/78= 0.2307
Pr(M|F) = Pr(M / F) / P(F) = 0.2307 / 0.3846 = 0.5998
Pr(F|M)= Pr(M / F) / P(M) = 0.2307 / 0.6153 = 0.3749
b) Since there is no new information regardinig single applicants
Pr(U) = Probability of single person getting the job = number of single applicants / total number of applicants
= 18+12/78 = 30/78 = 0.3846
Pr(V)= 48/78=0.6153
Now Pr(U/V) = 18/78 = 0.2307
Pr(U|V)= Pr(U/V)/Pr(V) = 0.2037/0.6153 = 0.3749
Pr(V|U)= Pr(U/V)/Pr(U)= 0.2307/0.3806 = 0.6061
Since Pr(U/V)=Pr(U)Pr(V) {when calculated exactly}
Thus U and V are independent
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