two fair coins. He wins $5 if 2 heads occur,$2 ifProblem#6: A player tosses1head occurs and $1 if no heads occur.(i) Find his expected winnings. (ii) Howmuch should he pay to play the game if it is to be fair?

When a fair coin is tossed twice S={HH, HT, TH, TT} Total number of possible cases =4 Probability of…

Answered: Problem#6: A player tosses two fair…

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

Section14.4: Expected Value

Problem 1E: CONCEPTS 1. If a game gives payoffs of 10 and 100 with probabilities 0.9 and 0.1, respectively, then...

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A Game of Chance A box contains 100 envelopes. Ten envelopes contain $10 each, ten contain $5 each, two are “unlucky", and the rest are empty. A player draws an envelope from the box and keeps whatever is in it. If a person draw an unlucky envelope, however, he must pay $100. What is the expectation of a person playing this game?
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.
CONCEPTS 1. If a game gives payoffs of 10 and 100 with probabilities 0.9 and 0.1, respectively, then the expected value of the game is E=0.9+0.1=

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Problem#6: A player tosses two fair coins. He wins $5 if 2 heads occur, $2 if 1head occurs and $1 if no heads occur. (i) Find his expected winnings. (ii) How much should he pay to play the game if it is to be fair?