Question

Finding Binomial Probabilities Mr. Taylor filled out a bracket for the NCAA National Tournament. Based on his knowledge of college basketball, he has a 0.45 probability of correctly picking the winner of a game in the tournament. The NCAA National Tournament has 32 first round games. Round each answer to 3 decimal places.

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 8 games correctly in the first round?

What is the probability Mr. Taylor will pick exactly 22 games incorrectly in the first round?

Answer 1

a)

Here, n = 32, p = 0.45, (1 - p) = 0.55 and x = 32
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 32)
P(x =32) = 32C32 * 0.45^32 * 0.55^0
= 0

b)

Here, n = 32, p = 0.45, (1 - p) = 0.55 and x = 8
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 8)
P(X = 8) = 32C8 * 0.45^8 * 0.55^24
P(X = 8) = 0.010

c)

Here, n = 32, p = 0.45, (1 - p) = 0.55 and x = 22
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 22)
P(X = 8) = 32C22 * 0.45^22 * 0.55^12
P(X = 8) = 0.004