A tosses one coin and B tosses two coins. The winner is the player who gets the

Question

A tosses one coin and B tosses two coins. The winner is the player who gets the most heads. In case of an equal number of heads A wins. (a) Compute the probability that B wins given that A gets 0 heads. (b) Compute the probability that B wins given that A gets 1 heads. (c) Compute the probability that B wins. (d) Change the game so that A tosses 2 coins and B tosses 3 coins. The winner is still the player who gets the most heads. In case of an equal number of heads A wins. Compute the probability that B wins in the new game.

Explanation / Answer

a) probability that B wins given that A gets 0 heads =P(B gets at least one heads) =1-P(B get no head) =1-(1/2)2

=3/4

b)probability that B wins given that A gets 1 heads. =P(B gets 2 heads) =(1/2)*(!/2) =1/4

c) probability that B wins =P(A get 0 head and B gets at least one head)+P(A get 1 head and B get 2 head)

=(1/2)*(3/4)+(1/2)*(1/4) =4/8 =1/2

d

probability that B wins in the new game=P(P(A get 0 head and B gets at least one head)+P(A get 1 head and B get 2 or more head+P(A get 2 head and B gets 3 heads )

=(1/4)*(1-1/8)+(1/2)*(1/2)+(1/4)*(1/8)=16/32 =1/2

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