A and B toss a pair of coins in turn, with A tossing first. A's objective...

A and B toss a pair of coins in turn, with A tossing first. A's objective is to obtain TT and B's is to obtain TH (or HT). The game ends when either player reaches his or her objective, and that player is declared the winner. Assuming that H appears with probability p=1/3 in each coin.

1) Find the probability that A is the winner

2) Find the expected number of tosses of the coins

Expert Solution

P(TT) = P(T)P(T) = (1-1/3)^2 = 4/9

P(TH) = P(HT) = 1/3 *2/3 = 2/9

P(TH or HT) = 4/9

P(HH or TT) = 1 - 4/9 = 5/9

hence probability that B does not win in any game = 5/9

a) S = 4/9 + (5/9)^2 * 4/9 + (5/9)^4 *4/9 + ...

= (4/9)/(1- (5/9)^2)

=0.64285

b) E(X) = 1/p = 1/(4/9) = 9/4 = 2.25

orchestra answered 2 years ago

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