Player A goes first and has probability p1 of making a basket on any attempt. Player B, who shoots second, has probability p2 of making a basket. So they go player A, then player B, then player A, then player B, and so on until one of them makes a basket. The attempts are independent of each other. a. Find the probability mass function of X, the total number of attempts until the game stops. b. What is the probability that player A wins? serian

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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The text outlines a scenario involving two players, A and B, who take turns attempting to make a basket. Player A shoots first and has a probability \( p_1 \) of making a basket on any attempt. Player B, who shoots second, has a probability \( p_2 \) of making a basket. The sequence of play is player A, then player B, and continues in this alternating pattern until one of them makes a basket.

Key points:
- The attempts by players are independent of each other.

Problems:
a. Determine the probability mass function of \( X \), which represents the total number of attempts until the game concludes.
b. Calculate the probability that player A wins.
Transcribed Image Text:The text outlines a scenario involving two players, A and B, who take turns attempting to make a basket. Player A shoots first and has a probability \( p_1 \) of making a basket on any attempt. Player B, who shoots second, has a probability \( p_2 \) of making a basket. The sequence of play is player A, then player B, and continues in this alternating pattern until one of them makes a basket. Key points: - The attempts by players are independent of each other. Problems: a. Determine the probability mass function of \( X \), which represents the total number of attempts until the game concludes. b. Calculate the probability that player A wins.
**Basketball Game Scenario**

6. Two people play a basketball game in the following way. They take turns shooting and stop when a basket is made. That is to say they take turns attempting a basket, and stop when the first basket is made.
Transcribed Image Text:**Basketball Game Scenario** 6. Two people play a basketball game in the following way. They take turns shooting and stop when a basket is made. That is to say they take turns attempting a basket, and stop when the first basket is made.
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