Answered: (i) If 3 dice are rolled, how many "6s"…

(i) If 3 dice are rolled, how many "6s" do you get on average? (ii) How many times on average do you have to toss a coin that gives "heads" with a probability of 1/2, to get "tails"?

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.CT: Chapter Test

Problem 14CT: An unbalanced coin weighted so that the probability of heads is 0.55. The coin is tossed ten times....

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Question

Bernoulli proofs:
(i) If 3 dice are rolled, how many “6s" do you get on average?
(ii) How many times on average do you have to toss a coin that gives "heads" with a probability of 1/2, to get "tails"?

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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).