SOLUTION: In a series of 5 games to be played between 2 equally matched teams, the first team to win 3 games becomes the champion. Team A has won the first game. The probability that team

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Question 976608: In a series of 5 games to be played between 2 equally matched teams, the first
team to win 3 games becomes the champion. Team A has won the first game. The
probability that team A will be the champion is ?
Is 3/5 incorrect?
Since there are 5 games, Team A won the first game. There are 4 more games left. Two more games till Team A wins or three more games till Team B wins. So obviously the probability of Team A winning is higher than Team B winning.
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
In a series of 5 games to be played between 2 equally matched teams, the first
team to win 3 games becomes the champion. Team A has won the first game. The
probability that team A will be the champion is ?
Is 3/5 incorrect?
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Binomial Problem with n = 5 and p(win) = 0.5
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P(A wins 2 of 4) = 4C2*0.5^2*0.5^2 = 6*0.25^2 = 0.375 = 3/8
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Cheers,
Stan H.
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Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
Here's a chart showing all of the possible combinations and probabilities for a 5 game series.
.
.
.

.
.
.
Since each team is equally matched, assume that the chance of A winning a game is 0.5.
So the probability of each row is just the product of the probabilities.
A three game series would have a probability of,

Four game series,

Five game series

Since A already won one game, start in the second column and add up the probabilities of A winning.
The sum of those probabilities is 0.34375.
Now this is out of 0.5 instead of 1.0 since half the games have been knocked out since A won the first.
So the probability of A winning given they won the first is,