Question

A coach recruits for a college team a star player who is currently a high school senior. In order to play next year, the senior must both complete high school with adequate grades and pass a standardized test. The coach estimates that the probability the athlete will fail to obtain adequate high school grades is $0.02$, that the probability the athlete will not pass the standardized test is $0.15$, and that these are independent events. According to these estimates, what is the probability that this recruit will be eligible to play in college next year?

Name: Problem 41, Chapter 3: Statistics for Business and Economics
Uploaded: 2021-12-25T16:26:02-08:00
Duration: 1 min 53 s
Channel: Christopher Stanley

   A coach recruits for a college team a star player who is currently a high school senior. In order to play next year, the senior must both complete high school with adequate grades and pass a standardized test. The coach estimates that the probability the athlete will fail to obtain adequate high school grades is $0.02$, that the probability the athlete will not pass the standardized test is $0.15$, and that these are independent events. According to these estimates, what is the probability that this recruit will be eligible to play in college next year?

Statistics for Business and Economics

Paul Newbold,… 8th Edition

Chapter 3, Problem 41

Instant Answer

Solved by Expert Christopher Stanley

12/25/2021

Step 1

This can be calculated using the formula for the probability of the union of two events, which is given by the sum of the probabilities of the two events minus the probability of their intersection. Since the two events are independent, their intersection is given Show more…

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A coach recruits for a college team a star player who is currently a high school senior. In order to play next year, the senior must both complete high school with adequate grades and pass a standardized test. The coach estimates that the probability the athlete will fail to obtain adequate high school grades is $0.02$, that the probability the athlete will not pass the standardized test is $0.15$, and that these are independent events. According to these estimates, what is the probability that this recruit will be eligible to play in college next year?

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Key Concepts

Independent Events

Independent events are events where the occurrence (or non-occurrence) of one event does not affect the probability of the other event occurring. This principle allows us to calculate the joint probability of both events happening by simply multiplying their individual probabilities.

Complementary Events

Complementary events refer to an event and its opposite, where the probabilities of the event and its complement add up to one. In many scenarios, it is easier to determine the probability of an event not happening (its complement) and subtracting from one to find the probability of success.

Multiplication Rule for Independent Events

The multiplication rule states that if two events are independent, the probability of both events occurring is the product of their individual probabilities. This rule is crucial when calculating the likelihood of a combined outcome where multiple independent conditions must be satisfied.

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