4. Suppose a game consists of rolling a die 12 times independently. You win $1 each time the upfaceof 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?(10Ad

We let Xbe the random variable that measures the gain of this game. Since we roll a die 12 times.…

Answered: 4. Suppose a game consists of rolling a…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

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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Similar questions

You toss two six-sided dice. What is the probability that the total of the two dice is 5?
Show that the probability of drawing a club at random from a standard deck of 52 playing cards is the same as the probability of drawing the ace of hearts at random from a set of four cards consisting of the aces of hearts, diamonds, clubs, and spades.
In Example 8, what is the probability that an employee chosen at random has 30 or more years of service?
Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an $8000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning (and that of B winning) if the game were to continue? The French mathematicians Pascal and Fermat corresponded about this problem, and both came to the same correct conclusion (though by very different reasoning's). Their friend Roberval disagreed with both of them. He argued that player A has probability of Winning, because the game can end in the four ways H, TH, TTH, TTT, and in three of these, A wins. Roberval’s reasoning was wrong. Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform this experiment 80 or more times, and estimate the probability that player A wins. Calculate the probability that player A wins. Compare with your estimate from part (a).

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