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 (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 25E
Related questions
Question
![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),](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F734d431c-c5fe-4366-a7d3-7661a31b1d15%2F8b2938f7-6e83-455f-a764-8743a8c15432%2F1l0in8o_processed.jpeg&w=3840&q=75)
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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