Question

Fred Poisson, the chief statistician at Disneyland, has found that $72 \%$ of the visitors go on the Jungle Cruise, $56 \%$ ride the Monorail, $60 \%$ take the Matterhorn ride, $50 \%$ go on the Jungle Cruise and ride the Monorail, $45 \%$ go on the Jungle Cruise and on the Matterhorn ride, $40 \%$ ride the Monorail and take the Matterhorn ride, and $30 \%$ take all three rides. Assuming Poisson's figures are correct, calculate the probability that a visitor to Disneyland will (a) go on at least one of the three rides. (b) ride the Monorail given that the Jungle Cruise was taken. (c) take the Matterhorn ride given that both the Jungle Cruise and Monorail rides were taken.

Name: Problem 23, Chapter 2: Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)
Uploaded: 2020-10-28T05:48:21-08:00
Duration: 2 min 19 s
Channel: Sherrie Fenner

   Fred Poisson, the chief statistician at Disneyland, has found that $72 \%$ of the visitors go on the Jungle Cruise, $56 \%$ ride the Monorail, $60 \%$ take the Matterhorn ride, $50 \%$ go on the Jungle Cruise and ride the Monorail, $45 \%$ go on the Jungle Cruise and on the Matterhorn ride, $40 \%$ ride the Monorail and take the Matterhorn ride, and $30 \%$ take all three rides. Assuming Poisson's figures are correct, calculate the probability that a visitor to Disneyland will
(a) go on at least one of the three rides.
(b) ride the Monorail given that the Jungle Cruise was taken.
(c) take the Matterhorn ride given that both the Jungle Cruise and Monorail rides were taken.

Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Arnold O. Allen 2nd Edition

Chapter 2, Problem 23

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Solved by Expert Sherrie Fenner

10/28/2020

Step 1

We are given the probabilities of visitors at Disneyland participating in three different rides, both individually and in combination. We need to find the probability that a visitor will (a) go on at least one of the three rides, (b) ride the Monorail given that Show more…

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Fred Poisson, the chief statistician at Disneyland, has found that $72 \%$ of the visitors go on the Jungle Cruise, $56 \%$ ride the Monorail, $60 \%$ take the Matterhorn ride, $50 \%$ go on the Jungle Cruise and ride the Monorail, $45 \%$ go on the Jungle Cruise and on the Matterhorn ride, $40 \%$ ride the Monorail and take the Matterhorn ride, and $30 \%$ take all three rides. Assuming Poisson's figures are correct, calculate the probability that a visitor to Disneyland will (a) go on at least one of the three rides. (b) ride the Monorail given that the Jungle Cruise was taken. (c) take the Matterhorn ride given that both the Jungle Cruise and Monorail rides were taken.

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Key Concepts

Inclusion-Exclusion Principle

This principle is used in probability theory to accurately compute the probability of the union of several events by summing their individual probabilities, then subtracting the probabilities of all pairwise intersections, adding back in the probabilities of triple intersections, and so on. It ensures that overlapping probabilities are not double-counted when determining the probability that at least one event occurs.

Conditional Probability

Conditional probability measures the likelihood of an event occurring given that another event has already occurred. It is calculated as the ratio of the probability of the intersection of the events to the probability of the conditioning event. This concept is essential when determining probabilities in a restricted sample space, such as finding the chance of one ride being taken given that another was already taken.

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