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O and are playing a game. The game has seven (7) rounds. They are initially located at "0" (marked as "x" in the graph below). For each round, they play rock-paper-scissors. If wins the game (which has probability), Awill make one step to the right, while remains at the location; if wins, or the game is draw (which has probability), O will make one step to the right, while A remains. After seven rounds, the winner is whichever who makes more steps. 0 1 2 3 4 5 6 7 (a) Let X, Y be the position (0 to 7) of and after seven rounds. What is the distribution of X, Y. Give the relevant parameters. (b) Compute the expected value of X, Y. (c) Find the probability that X ≤ 2. Express your answer up to 3rd decimal place.

O and are playing a game. The game has seven (7) rounds. They are initially located at "0" (marked as "x" in the graph below). For each round, they play rock-paper-scissors. If wins the game (which has probability), Awill make one step to the right, while remains at the location; if wins, or the game is draw (which has probability), O will make one step to the right, while A remains. After seven rounds, the winner is whichever who makes more steps. 0 1 2 3 4 5 6 7 (a) Let X, Y be the position (0 to 7) of and after seven rounds. What is the distribution of X, Y. Give the relevant parameters. (b) Compute the expected value of X, Y. (c) Find the probability that X ≤ 2. Express your answer up to 3rd decimal place.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 61E: Roulette American roulette is a game in which a wheel turns on a spindle and is divided into 38...
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O and A are playing a game. The game has seven (7) rounds. They are initially located at "0" (marked as "x" in the graph below). For each round, they play rock-paper-scissors. If wins the game (which has probability), will make one step to the right, while remains at the location; if will make remains. After seven rounds, the winner is whichever one step to the right, while who makes more steps. X 0 1 2 3 4 5 6 7 (a) Let X, Y be the position (0 to 7) of O and A after seven rounds. What is the distribution of X, Y. Give the relevant parameters. (b) Compute the expected value of X, Y. (c) Find the probability that X ≤ 2. Express your answer up to 3rd decimal place. (d) Find the probability that wins the game after seven rounds. Express your answer up to 3rd decimal place. (Hint: what is the sum X+Y?) (e) After the game ends, the loser will have to play the winner x pieces of treat, is at where x is the difference of their final position. E.g., if O is at 6, and pays 1, then 6-1= 5 pieces of treats. Let Z be the number of treats earned by O in this game (≤0 if he loses). Find E[Z]. wins, or the game is draw (which has probability),
Transcribed Image Text:O and A are playing a game. The game has seven (7) rounds. They are initially located at "0" (marked as "x" in the graph below). For each round, they play rock-paper-scissors. If wins the game (which has probability), will make one step to the right, while remains at the location; if will make remains. After seven rounds, the winner is whichever one step to the right, while who makes more steps. X 0 1 2 3 4 5 6 7 (a) Let X, Y be the position (0 to 7) of O and A after seven rounds. What is the distribution of X, Y. Give the relevant parameters. (b) Compute the expected value of X, Y. (c) Find the probability that X ≤ 2. Express your answer up to 3rd decimal place. (d) Find the probability that wins the game after seven rounds. Express your answer up to 3rd decimal place. (Hint: what is the sum X+Y?) (e) After the game ends, the loser will have to play the winner x pieces of treat, is at where x is the difference of their final position. E.g., if O is at 6, and pays 1, then 6-1= 5 pieces of treats. Let Z be the number of treats earned by O in this game (≤0 if he loses). Find E[Z]. wins, or the game is draw (which has probability),
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