Binomial Distribution Suppose the probability of beating you

Binomial Distribution Suppose the probability of beating your friend in a video game is constant at 0.85. The outcome of each game is independent, and either you or your friend have to win each game. 9. What is the probability that you beat your friend in 4 out of 5 games? Round your answer to two decimnal places. Page 7

Solution

p = 0.85, n = 5 and x = 4

Probability of 4 successes is given by the binomial probability distribution:

P (x = 4) = ⁿC_x x p^x x (1 - p)^{(n - x)}

P (x = 4) = 0.3915