SOLUTION: goliath and David play a game in which there are no ties. Each player is likely to win each game. The first player to win 4 games becomes the champion, and no further games are pla

Question 1110139: goliath and David play a game in which there are no ties. Each player is likely to win each game. The first player to win 4 games becomes the champion, and no further games are played. Goliath wins the first 2 games. What is the probability that David becomes the champion?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the probability of winning is 1/2.
the probability of losing is 1/2.

david has to win 4 games and can lose at most 1 game in order for david to become the champion.

in the following table, 1 means a win for david and 0 means a loss for david.

the probability for a 1 or a 0 is equal to 1/2.

p(1,1,1,1) = (1/2) ^ 4 = 1/16
p(1,1,1,0,1) = (1/2)^5 = 1/32
p(1,1,0,1,1) = (1/2)^5 = 1/32
p(1,0,1,1,1) = (1/2)^5 = 1/32
p(0,1,1,1,1) = (1/2)^5 = 1/32

the probability of david becoming the champion is therefore 1/16 + 4/32 = 6/32 = 3/16.

in decimal form, that's .1875.

that's my take.

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