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Suppose that a basketball player's success in free-throw shooting can be described with a Markov chain. If the player made the last free throw, then she is four times more likely to make the next free throw as miss it. If the player missed her last free throw, then she is equally likely to make or miss the next free throw. 1. Find the transition matrix for the Markov chain. 2. If she made her last free throw, what is the probability she makes the next two in a row, for a total of three in a row? 3. If the she makes he third free throw, what is the probability she makes her fifth free throw? 4. If she misses her first free throw, what is the probability she also misses her third and fifth free throw?

Suppose that a basketball player's success in free-throw shooting can be described with a Markov chain. If the player made the last free throw, then she is four times more likely to make the next free throw as miss it. If the player missed her last free throw, then she is equally likely to make or miss the next free throw. 1. Find the transition matrix for the Markov chain. 2. If she made her last free throw, what is the probability she makes the next two in a row, for a total of three in a row? 3. If the she makes he third free throw, what is the probability she makes her fifth free throw? 4. If she misses her first free throw, what is the probability she also misses her third and fifth free throw?

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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Suppose that a basketball player's success in free-throw shooting can be described with a Markov chain. If the player made the last free throw, then she is four times more likely to make the next free throw as miss it. If the player missed her last free throw, then she is equally likely to make or miss the next free throw. 1. Find the transition matrix for the Markov chain. 2. If she made her last free throw, what is the probability she makes the next two in a row, for a total of three in a row? 3. If the she makes he third free throw, what is the probability she makes her fifth free throw? 4. If she misses her first free throw, what is the probability she also misses her third and fifth free throw?
Transcribed Image Text:Suppose that a basketball player's success in free-throw shooting can be described with a Markov chain. If the player made the last free throw, then she is four times more likely to make the next free throw as miss it. If the player missed her last free throw, then she is equally likely to make or miss the next free throw. 1. Find the transition matrix for the Markov chain. 2. If she made her last free throw, what is the probability she makes the next two in a row, for a total of three in a row? 3. If the she makes he third free throw, what is the probability she makes her fifth free throw? 4. If she misses her first free throw, what is the probability she also misses her third and fifth free throw?
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