Question

In 29 of the first 52 Super Bowl games in professional football (56%), the winning team won by over 9 points (double digits). Suppose we randomly select 10 Super Bowl games out of the first 52 and count the number in which the winning team had a double digit victory. Assume independence between the Super Bowls selected- consider them to be chosen with replacement.

a) Define the random variable, x, and give the name and important parameters of the probability distribution.

b) Find the probability that more than three but fewer than eight of the games were won by double digits. State the probability statement in terms of X and show all work.

Answer 1

a) X is hypergeometric distribution

N = 52

k = 29

n = 10

b) P(X = x) = [ _kC_x ] [ _N-kC_n-x ] / [ _NC_n ]

P(3 < X < 8) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

                    = 29C4 * 23C6 / 52C10 + 29C5 * 23C5 / 52C10 + 29C6 * 23C4 / 52C10 + 29C7 * 23C3 / 52C10

                    = 0.8447