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 55% of all potential purchasers select a day visit, 25% choose a one-night visit, and 20% opt for a two-night visit. In addition, 10% of day visitors ultimately make a purchase, 25% of night visitors make a purchase, and 20% of those visiting for two nights make a purchase. Suppose a visitor is randomly selected. What is the probability that the visitor makes a purchase

Answer 1

0.1575 = 15.75% probability that the visitor makes a purchase

Explanation:

We have these following probabilities:

55% probability that a visitor selects a day visit, and in this case, 10% probability of making a purchase.

25% probability that a visitor chooses a one-night visit, and in this case, 25% probability of making a purchase.

20% probability that a visitor chooses for a two night visit, and in this case, 20% probability of making a purchase.

What is the probability that the visitor makes a purchase

`p = 0.55*0.1 + 0.25*0.25 + 0.2*0.2 = 0.1575`

0.1575 = 15.75% probability that the visitor makes a purchase