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Manu and Janani are playing a coin toss game with a fair penny. Man.pdf

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Manu and Janani are playing a coin toss game with a fair penny. Manu get a point if the penny lands on heads, Janani get a point if the penny lands on tails. THe score is Janani 9, Manu 7, in a game to 10 points. WHat is the probability that Janani will win the game? Express your answer as a common fraction. Solution The probability that J will win is one minus the probability that he will lose because there are only two possible outcomes. In order for J to lose, M must win. In order for M to win, the next three coin tosses in a row must result in heads. The probability that three consecutive tosses of a fair coin will be heads is: 1/2*1/2*1/2=1/8 Since the probability that M will win is , the probability that M will lose, which is the same as the probability that J will win is 1-1/8=7/8.

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Manu and Janani are playing a coin toss game with a fair penny. Manu get a point if the penny lands on heads, Janani get a point if the penny lands on tails. THe score is Janani 9, Manu 7, in a game to 10 points. WHat is the probability that Janani will win the game? Express your answer as a common fraction. Solution The probability that J will win is one minus the probability that he will lose because there are only two possible outcomes. In order for J to lose, M must win. In order for M to win, the next three coin tosses in a row must result in heads. The probability that three consecutive tosses of a fair coin will be heads is: 1/2*1/2*1/2=1/8 Since the probability that M will win is , the probability that M will lose, which is the same as the probability that J will win is 1-1/8=7/8

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Manu and Janani are playing a coin toss game with a fair penny. Man.pdf

  • 1. Manu and Janani are playing a coin toss game with a fair penny. Manu get a point if the penny lands on heads, Janani get a point if the penny lands on tails. THe score is Janani 9, Manu 7, in a game to 10 points. WHat is the probability that Janani will win the game? Express your answer as a common fraction. Solution The probability that J will win is one minus the probability that he will lose because there are only two possible outcomes. In order for J to lose, M must win. In order for M to win, the next three coin tosses in a row must result in heads. The probability that three consecutive tosses of a fair coin will be heads is: 1/2*1/2*1/2=1/8 Since the probability that M will win is , the probability that M will lose, which is the same as the probability that J will win is 1-1/8=7/8