three coins in a bag. Coin 1 (call it C1) is a fair coin, coin 2 (call it C2) and coin 3|(call it C3) are both biased with coin 2 having heads on both sides and coin 3 having tails onboth sides. You randomly chose one and tossed it twice.(a)the probability of obtaining two heads from C1, i.e., the fair coin.(b)the probability of obtaining two heads from C2.(c)* the probability of obtaining two heads.(d) Suppose you obtained two heads but you didn't know which coin was chosen. Whichtheorem can help find the conditional probability that the fair coin is chosen given twoheaus were obtained?(e) Find the conditional probability that the fair coin is chosen given two heads were ob-tained.

Answered: Image /qna-images/answer/2de5e76d-fd33-4afe-9d3f-d8ac537837dc.jpg

Answered: (a) the probability of obtaining two…

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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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).
Balls in a Jar Jar A contains three red balls and four white balls. Jar B contains five red balls and two white balls. Which one of the following ways of randomly selecting balls gives the greatest probability of drawing two red balls? (i) Draw two balls from jar B. (ii) Draw one ball from each jar. (iii) Put all the balls in one jar, and then draw two balls.
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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