SOLUTION: The probability that Barca wins a game with A.C. Milan is 0.2. Suppose they play 7 games. What is the probability that A.C. Milan wins at least four of the games?

Hi

Note: The probability of x successes in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. 

In this case p = .2 and q = .8

nCx = 

P(winning at least 4 of 7 games) = 1-P(no wins) -P(1 win) - P(2 wins) - P(3wins)

P(no wins) = (.8)^7 = .2097

P(1 win) = 7(.2)^1*(.8)^6 = .3670

P(2 wins)=  21(.2)^2*(.8)^5 = .2753

P(3wins)= 35(.2)^3*(.8)^4 = .1147

P(winning at least four games) = 1 -.9667 = .0333