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

ID: 2957564 • Letter: A

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) = 0.7, P(B) = 0.27, and P(A and B) = 0.04.

What is the conditional probability (±0.01) that a student is local, given that he or she is less than 25 years old?

What is the probability (±0.01) that the student is at least 25 years old and not local?  

Explanation / Answer

P(A and B) = 0.04, P(A) = 0.70, so P(A and not B) = 0.70-0.04 = 0.66

P(B) = 0.27, so P(B and not A) = 0.27-0.04 = 0.23

P(B|not A) = P(B and not A)/P(not A) = 0.23/0.30 = 0.77 [this is first answer]

P(A|not B) = P(A and not B)/P(not B) = 0.66/0.73 = 0.90 [this is second answer]