A study of the students taking distance learning courses at a university finds t

Question

A study of the students taking distance learning courses at a university finds that they are mostly older students not living in the university town. Choose a distance learning student at random. Let A be the event that the student is 25 years old or older and B the event that the student is local. The study finds that P(A) = 0.68, P(B) = 0.29, and P(A and B) = 0.03. Using these settings, what is the conditional probability that a student is local, given that he or she is less than 25 years old? (Use 3 decimal places.)

Explanation / Answer

here we have A be the event that the student is 25 years old or older

so Ac is the event that the student is less than 25 years old

B be the event that the student is local.

given that P[A]=0.68   P[B]=0.29 and P[A and B]=0.03

so the conditional probability that a student is local, given that he or she is less than 25 years old is

P[B|Ac]=P[Ac and B]/P[Ac]={P[B]-P[A and B]}/{1-P[A]}={0.29-0.03}/{1-0.68}=0.812 [answer]

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