Alonzo is playing a game of chance in which he rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random.This game is this: Alonzo rolls the number cube once. He wins $1 if a 1 is rolled, $2 if a 2 is rolled, and $3 if a 3 is rolled. He loses $0.50 if a 4, 5, or 6 is rolled.(a)Find the expected value of playing the game. dollars (b)What can Alonzo expect in the long run, after playing the game many times? Alonzo can expect to gain money. Hecanexpecttowindollarsperroll. Alonzo can expect to lose money. Hecanexpecttolosedollarsperroll. Alonzo can expect to break even (neither gain nor lose money).

Answered: Image /qna-images/answer/266dc443-95d7-439d-829f-a852dfa5a298.jpg

Answered: (a) Find the expected value of playing…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.FOM: Focus On Modeling: The Monte Carlo Method

Problem 3P: Dividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if...

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Roulette American roulette is a game in which a wheel turns on a spindle and is divided into 38 pockets. Thirty-six of the pockets are numbered 1-36, of which half are red and half are black. Two of the pockets are green and are numbered 0 and 00 (see figure). The dealer spins the wheel and a small ball in opposite directions. As the ball slows to a stop, it has an equal probability of landing in any of the numbered pockets. (a) Find the probability of landing in the number 00 pocket. (b) Find the probability of landing in a red pocket. (c) Find the probability of landing in a green pocket or a black pocket. (d) Find the probability of landing in the number 14 pocket on two consecutive spins. (e) Find the probability of landing in a red pocket on three consecutive spins.
Dividing a JackpotA game between two players consists of tossing a 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 8,000 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 Mathematician Pascal and Fermat corresponded about this problem, and both came to the same correct calculations though by very different reasonings. Their friend Roberval disagreed with both of them. He argued that player A has probability 34 of winning, because the game can end in the four ways H, TH, TTH, TTT and in three of these, A wins. Robervals reasoning was wrong. a Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform the experiment 80 or more times, and estimate the probability that player A wins. bCalculate the probability that player A wins. Compare with your estimate from part a.

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(a) Find the expected value of playing the game. dollars (b) What can Alonzo expect in the long run, after playing the game many times?