Question

On New Year's Eve, the probability of a person driving while intoxicated or having a driving accident is $0.35 .$ If the probability of driving while intoxicated is 0.32 and the probability of having a driving accident is $0.09,$ find the probability of a person having a driving accident while intoxicated.

Name: Problem 74, Chapter 11: Algebra and Trigonometry
Uploaded: 2020-06-10T06:23:29-08:00
Duration: 1 min 21 s
Channel: Ankit Gupta
Description: On New Year's Eve, the probability of a person driving while intoxicated or having a driving accident is 0.35 . If the probability of driving while intoxicated is 0.32 and the probability of having a driving accident is 0.09, find the probability of a person having a driving accident while intoxicated.

   On New Year's Eve, the probability of a person driving while intoxicated or having a driving accident is $0.35 .$ If the probability of driving while intoxicated is 0.32 and the probability of having a driving accident is $0.09,$ find the probability of a person having a driving accident while intoxicated.

Algebra and Trigonometry

Robert Blitzer 6th Edition

Chapter 11, Problem 74

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Solved by Expert Ankit Gupta

06/10/2020

Step 1

32, the probability of having a driving accident (B) is 0.09, and the probability of either event occurring (A or B) is 0.35. Show more…

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On New Year's Eve, the probability of a person driving while intoxicated or having a driving accident is $0.35 .$ If the probability of driving while intoxicated is 0.32 and the probability of having a driving accident is $0.09,$ find the probability of a person having a driving accident while intoxicated.

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Key Concepts

Intersection of Events

This is the event where two events occur simultaneously. Determining the probability of the intersection is essential in situations where events overlap and is computed by rearranging the addition rule if the union probability is known.

Addition Rule of Probability

A fundamental principle in probability theory, the addition rule states that the probability of the union of two events equals the sum of the probabilities of each event minus the probability of their intersection. This rule is vital for solving problems where events are not mutually exclusive.

Union of Events

This concept refers to the event that at least one of two events occurs. The probability of the union of events is found by summing the probabilities of the individual events and then subtracting the probability of their intersection to avoid double counting.

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