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 20% of all potential purchasers select a day visit, 50% choose a one-night visit, and 30% opt for a two-night visit. In addition, 10% of day visitors ultimately make a purchase, 40% of one-night visitors buy a unit, and 40% of those visiting for two nights decide to buy. Suppose a visitor is randomly selected and is found to have made a purchase. How likely is it that this person made a day visit

Answer 1

Answer:

0.143.

Step-by-step explanation:

The first step to take in answering this question is to take or determine the probability in each cases, multiply and sum them up. Therefore, let us delve right into the solution of this problem;

[a]. Historical data indicates that 20% of all potential purchasers select a day visit. Thus, the probability that potential purchasers selects a day visit = 0.20.

[b]. Historical data indicates that 50% choose a one-night visit.  Thus, the probability that potential purchasers selects a one-night visit= 0.50.

[c]. Historical data indicates that 30% of all potential purchasers opt for a two-night visit. Thus, the probability that potential purchasers  opt for a two-night visit = 0.30.

[d].Historical data indicates that 10% of day visitors ultimately make a purchase. Thus, the probability that a day visitors ultimately make a purchase = 0.1.

[e]. The probability for  40% of one-night visitors buy a unit =0.4

[f]. The probability for  40% of two nights decide to buy =0.4.

STEP ONE: Determine the probability that the visitor makes a purchase.

The probability that the visitor makes a purchase = [a] × [d] + [b] × [e] + [c] × [f]. = 0.2 × 0.1 + 0.5 × 0.4 + 0.3 × 0.4 = 0.02 + 0.02 + 0.12 = 0.14.

STEP TWO: Determine How likely is it that this person made a day visit.

0.2 × 0.1/ 0.14 = 0.1428571428571429