2. A large operator of timeshare complexes requires anyone interested in making

Question

2. A large operator of timeshare complexes requires anyone interested in making a purchase to first visit the site of interest. Historical data indicates that 40% of all potential purchasers select a day visit, 60% choose a one-night visit. In addition, 10% of day visitors ultimately make a purchase while 30% for one-night visitors. It might be helpful to draw a probability tree.

A. What is the probability that a randomly selected visitor does not make a purchase?

B. If you learn that a visitor made a purchase, how likely is it that he or she has a night visit?

Explanation / Answer

Probability of night visit, P(N) = 0.6 and P(N') = 0.4
Night visitor make purchase and do not make purchase, P(P|N) = 0.3 , P(P'|N) = 0.7
Day visitor make purchase and do not make purchase, P(P|N') = 0.1, P(P'|N') = 0.9

A)
P(Does not make a purchase) = P(N')*P(P|N') + P(N)*P(P|N)
= 0.4*0.9 + 0.6*0.7
= 0.78

B)
P(Make a purchase) = 1 - 0.78 = 0.22
P(N | P) = 0.6*0.3/0.22 = 0.8182

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