SOLUTION: two evenly matched soccer teams are playing a 7- game tournament. What is the probability that the first team will win 5 out of 7 games?

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Question 951259: two evenly matched soccer teams are playing a 7- game tournament. What is the probability that the first team will win 5 out of 7 games?
Answer by mathmate(429) About Me  (Show Source):
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Given:
Two soccer teams.
Each has equal chance of winning (p=0.50).
They play 7 games.
Need probability of first team winning exactly 5 out of 7 games.

Solution:
First team has known and constant probability of winning (p=0.5)
Number of trials (games) is known (n=7)
Games are (assumed) independent.
Under these conditions, binomial distribution applies.

r=5 (number of successes)

P(X=5)=nCr%2Ap%5Er%2A%281-p%29%5E%28n-r%29
=7%21%2F%285%212%21%29%2A%281%2F2%29%5E5%2A%281%2F2%29%5E2
=21%2F128
=0.164 approximately

Answer
Probability of first team winning five games out of seven is approximately 0.164