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

Ans:

P(day visitors)=0.4

P(One night visitors)=0.6

P(purchase/day visitor)=0.1

P(purchase/one night visitor)=0.3

a)P(purchase)=0.1*0.4+0.3*0.6=0.04+0.18=0.22

b)P(day visitor/purchase)=(0.1*0.4)/0.22=0.04/0.22=0.182

c)For A and B to be independent:

P(A and B)=P(A)*P(B)

P(day visit and purchase)=0.1*0.4=0.04

P(day visitors)*P(purchase)=0.4*0.22=0.088

Both are not equal,hence A and B are not independent.

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