4. Suppose a game consists of rolling a die 12 times independently. You win $1 each time the upface of the die is 2, 3, 5, or 6. Let X be the random variable that measures the gain of this game. (a) What is the probability of winning $0 in this game? (Z) (b) What (b) What is the probability of winning exactly $1 in this game? (c) What is the probability of gaining at least $1 in this game? (d) What is the expected gain of this game? (e) What is the variance of X? (10 Ad
4. Suppose a game consists of rolling a die 12 times independently. You win $1 each time the upface of the die is 2, 3, 5, or 6. Let X be the random variable that measures the gain of this game. (a) What is the probability of winning $0 in this game? (Z) (b) What (b) What is the probability of winning exactly $1 in this game? (c) What is the probability of gaining at least $1 in this game? (d) What is the expected gain of this game? (e) What is the variance of X? (10 Ad
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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Question
![4. Suppose a game consists of rolling a die 12 times independently. You win $1 each time the upface
of the die is 2, 3, 5, or 6. Let X be the random variable that measures the gain of this game.
(a) What is the probability of winning $0 in this game?
(Z)
(b) What
(b) What is the probability of winning exactly $1 in this game?
(c) What is the probability of gaining at least $1 in this game?
(d) What is the expected gain of this game?
(e) What is the variance of X?
(10
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Transcribed Image Text:4. Suppose a game consists of rolling a die 12 times independently. You win $1 each time the upface
of the die is 2, 3, 5, or 6. Let X be the random variable that measures the gain of this game.
(a) What is the probability of winning $0 in this game?
(Z)
(b) What
(b) What is the probability of winning exactly $1 in this game?
(c) What is the probability of gaining at least $1 in this game?
(d) What is the expected gain of this game?
(e) What is the variance of X?
(10
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