Question

Mr. Taylor filled out a bracket for the NCAA National Tournament. Based on his knowledge of college basketball, he has a 0.46 probability of guessing any one game correctly. What is the probability Mr. Taylor will pick all 32 of the first round games correctly? What is the probability Mr. Taylor will pick exactly 12 games correctly in the first round? What is the probability Mr. Taylor will pick exactly 25 games incorrectly in the first round?

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

P(guessing correctly), p = 0.46

q = 1 - p = 0.54

Number of trials, n = 32

P(Mr. Taylor will pick all 32 of the first round games correctly) = 0.46³²

= 1.6153x10^-11

P(Mr. Taylor will pick exactly 12 games correctly) = P(X = 12)

= 32C12 x 0.46¹² x 0.54²⁰

= 0.09009

P(Mr. Taylor will pick exactly 25 games incorrectly in the first round) = P(Mr. Taylor will pick exactly 7 games correctly)

= P(X = 7)

= 32C7 x 0.46⁷ x 0.54²⁵

= 0.00299