A large operator of timeshare complexes requires anyone interested in making a p

Question

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 made a purchase? B. If you learn that a visitor made a purchase, how likely is it that he or she has a day visit? C. Consider the event A = {a visitor had a day visit} and the event B = {a visit made a purchase}. Are these two events independent? Justify your answer for full credits.

Explanation / Answer

a) Probability = 0.4*0.1 + 0.6*0.3 = 0.22

b) Probability = (0.4*0.1)/(0.4*0.1+0.6*0.3) = 0.04/0.22 = 0.1818

c) In the case where events A and B are independent(where event A has no effect on the probability ofevent B), the conditional probability of event B given event A is simply the probability of event B, that is P(B).

So, here these are not independent

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