A and B are playing a coin-tossing game with a fair coin. If the coin lands on heads, B will give A one coin. If the coin lands on tails, A will give Ba coin. A has 500 coins and B starts with 50 coins. The game is played until either A or B loses all the capital. (a) What is the probability that B wins the game? (b) Suppose the coin is not fair. Let p be the probability that B wins and individual toss. What should p be so that the game is fair, i.e., the probability for B to win the game is 1/2?

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A and B are playing a coin-tossing game with
a fair coin. If the coin lands on heads, B will
give A one coin. If the coin lands on tails, A
will give Ba coin. A has 500 coins and B starts
with 50 coins. The game is played until either
A or B loses all the capital.
(a) What is the probability that B wins the
game?
(b) Suppose the coin is not fair. Let p be the
probability that B wins and individual toss.
What should p be so that the game is fair, i.e.,
the probability for B to win the game is 1/2?
Transcribed Image Text:A and B are playing a coin-tossing game with a fair coin. If the coin lands on heads, B will give A one coin. If the coin lands on tails, A will give Ba coin. A has 500 coins and B starts with 50 coins. The game is played until either A or B loses all the capital. (a) What is the probability that B wins the game? (b) Suppose the coin is not fair. Let p be the probability that B wins and individual toss. What should p be so that the game is fair, i.e., the probability for B to win the game is 1/2?
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