Question

The probability that concert tickets are available by telephone is $0.92 .$ For the same event, the probability that tickets are available through a Web site is $0.95 .$ Assume that these two ways to buy tickets are independent. What is the probability that someone who tries to buy tickets through the Web and by phone will obtain tickets?

Name: Problem 209, Chapter 2: Applied Statistics and Probability for Engineers
Uploaded: 2021-08-09T01:06:56-08:00
Duration: 1 min
Channel: Maxime Rossetti
Description: The probability that concert tickets are available by telephone is 0.92 . For the same event, the probability that tickets are available through a Web site is 0.95 . Assume that these two ways to buy tickets are independent. What is the probability that someone who tries to buy tickets through the Web and by phone will obtain tickets?

   The probability that concert tickets are available by telephone is $0.92 .$ For the same event, the probability that tickets are available through a Web site is $0.95 .$ Assume that these two ways to buy tickets are independent. What is the probability that someone who tries to buy tickets through the Web and by phone will obtain tickets?

Applied Statistics and Probability for Engineers

Douglas C.… 6th Edition

Chapter 2, Problem 209

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Solved by Expert Maxime Rossetti

08/09/2021

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92$ and the probability of getting tickets over the web is given as $0.95$. Show more…

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The probability that concert tickets are available by telephone is $0.92 .$ For the same event, the probability that tickets are available through a Web site is $0.95 .$ Assume that these two ways to buy tickets are independent. What is the probability that someone who tries to buy tickets through the Web and by phone will obtain tickets?

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Key Concepts

Independent Events

This concept means that the occurrence or non-occurrence of one event does not have any effect on the occurrence of another event. In the context of probability, this allows us to calculate the joint probability of two events by multiplying their individual probabilities, which simplifies the analysis of combined scenarios.

Multiplication Rule

The multiplication rule states that the probability of two independent events both occurring is the product of their individual probabilities. This fundamental principle is used to compute joint probabilities, especially when events do not influence each other.

Inclusion-Exclusion Principle

The inclusion-exclusion principle is used to determine the probability of at least one of several events occurring. It does this by adding the probabilities of the individual events and then subtracting the probability of their intersection to account for any overlap, ensuring that shared outcomes are not counted twice.

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