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, 20% of day visitors ultimately make a purchase, 50% 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? (Round your answer to three decimal places.) How likely is it that this person made a one-night visit? (Round your answer to three decimal places.) How likely is it that this person made a two-night visit? (Round your answer to three decimal places.)

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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, 20% of day visitors ultimately make a purchase, 50% 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? (Round your answer to three decimal places.)
How likely is it that this person made a one-night visit? (Round your answer to three decimal places.)
How likely is it that this person made a two-night visit? (Round your answer to three decimal places.)
Transcribed Image Text: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, 20% of day visitors ultimately make a purchase, 50% 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? (Round your answer to three decimal places.) How likely is it that this person made a one-night visit? (Round your answer to three decimal places.) How likely is it that this person made a two-night visit? (Round your answer to three decimal places.)
Expert Solution
Step 1

Let us define some events 

A : a person makes day visit.

B : a person makes a one-night visit.

C : a person makes a two-night visit.

E : a person makes a purchase.

It is given that

P(A) = 0.20, P(B) = 0.50, P(C) = 0.30

P(E|A) = 0.20, P(E|B) = 0.50, P(E|C) = 0.40

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