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Probability
At the end of regulation time, a basketball team is trailing by one point and a player goes to the line for free throws. If the player makes exactly one free throw, the game goes into overtime. The probability that the first free throw is good is ½. However, if the first attempt is good, the player relaxes and the second attempt is good with probability ¾. However, if the player misses the first attempt, the added pressure reduces the success probability to ¼. What is the probability that the game goes overtime? (Hint: You obviously can see the dependence between the first and the second shot, your solution should be done using the conditional probability concept)

At the end of regulation time, a basketball team is trailing by one point and a player goes to the line for free throws. If the player makes exactly one free throw, the game goes into overtime. The probability that the first free throw is good is ½. However, if the first attempt is good, the player relaxes and the second attempt is good with probability ¾. However, if the player misses the first attempt, the added pressure reduces the success probability to ¼. What is the probability that the game goes overtime? (Hint: You obviously can see the dependence between the first and the second shot, your solution should be done using the conditional probability concept)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Free Throws and Conditional Probability** At the end of regulation time, a basketball team is trailing by one point and a player goes to the line for free throws. If the player makes exactly one free throw, the game goes into overtime. The probability that the first free throw is good is \( \frac{1}{2} \). However, if the first attempt is good, the player relaxes and the second attempt is good with probability \( \frac{3}{4} \). However, if the player misses the first attempt, the added pressure reduces the success probability to \( \frac{1}{4} \). **Problem:** What is the probability that the game goes into overtime? **Hint:** You obviously can see the dependence between the first and the second shot, so your solution should be done using the concept of conditional probability.
Transcribed Image Text:**Free Throws and Conditional Probability** At the end of regulation time, a basketball team is trailing by one point and a player goes to the line for free throws. If the player makes exactly one free throw, the game goes into overtime. The probability that the first free throw is good is \( \frac{1}{2} \). However, if the first attempt is good, the player relaxes and the second attempt is good with probability \( \frac{3}{4} \). However, if the player misses the first attempt, the added pressure reduces the success probability to \( \frac{1}{4} \). **Problem:** What is the probability that the game goes into overtime? **Hint:** You obviously can see the dependence between the first and the second shot, so your solution should be done using the concept of conditional probability.
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