Question 951259
  
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*p^r*(1-p)^(n-r)}}}
={{{7!/(5!2!)*(1/2)^5*(1/2)^2}}}
={{{21/128}}}
=0.164 approximately
  
Answer
Probability of first team winning five games out of seven is approximately 0.164