×
Log in to StudySoup
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 2 - Problem 65e
Join StudySoup for FREE
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 2 - Problem 65e

Already have an account? Login here
×
Reset your password

A large operator of timeshare complexes requires anyone

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 65E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

4 5 1 328 Reviews
30
3
Problem 65E

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, 30% of one night visitors buy a unit, and 20% 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? A one-night visit? A two-night visit?

Step-by-Step Solution:
Step 1 of 3

Solution: Step1: Here based on the given data 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, 30% of one night visitors buy a unit, and 20% of those visiting for two nights decide to buy. A visitor is randomly selected and is found to have a made a purchase. Step2: a) We have to find the probability that selected person made a day visit. Here it is given that among 20% of day visitors 10% makes a purchase. Also among 50% of one- night visitors 30% purchase a unit. And among 30% of two- night visitors 20% makes a purchase. So based on this given information we can make probability table. Purchase yes No total Day visit .02 .18 .2 Visit .15 .35 .5 One-night visit .06 .24 .3 Two-night visit It is given that the randomly selected person made a purchase. Let A be the event that selected visitor made a purchase.And also lets define the events E1: The selected person made a day visit E2: The selected visitor made a one-night visit E3: The selected visitor made a two-night visit. So by bayes theorem the probability that selected the selected visitor made a day- visit. P(selected visitor made a day- visit given that visitor made a purchase)= (E1/A)= P(A/E1) × P(E1) P(A/E1)× P(E1)+P(A/E2)×P(E2)+P(A/E3)×P(E3) Here from the table P(A/E1)= .02 P(A/E2)= .15 P(A/E3) = .06 And also P(E1) = .2 P(E2) = .5 P(E3) = .3 So (E1/A) = .02×.2 .15×.5+.02×.2.+.06×.3 = 0.041 Step3 : b) P(selected visitor made a one-night visit given that visitor made a purchase)= P(A/E2) × P(E2) P(E2/A)= P(A/E1)× P(E1)+P(A/E2)×P(E2)+P(A/E3)×P(E3) So .15×.25 (E2/A) = .15×.5+.02×.2.+.06×.3 = 0.773 c) P(selected visitor made a two-night visit given that visitor made a purchase)= P(A/E3) × P(E3) P(E3/A)= P(A/E1)× P(E1)+P(A/E2)×P(E2)+P(A/E3)×P(E3) So (E3/A) = .06×.3 .15×.5+.02×.2.+.06×.3 = 0.1855

Step 2 of 3

Chapter 2, Problem 65E is Solved
Step 3 of 3

Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Since the solution to 65E from 2 chapter was answered, more than 885 students have viewed the full step-by-step answer. The answer to “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, 30% of one night visitors buy a unit, and 20% 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? A one-night visit? A two-night visit?” is broken down into a number of easy to follow steps, and 105 words. The full step-by-step solution to problem: 65E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. This full solution covers the following key subjects: visit, night, day, Purchase, Buy. This expansive textbook survival guide covers 18 chapters, and 1582 solutions.

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

A large operator of timeshare complexes requires anyone