Binomial and geometric experiments

Question

She will roll a die five times, and wants to know the probability of getting exactly two threes. Define the variables: Probability of success(rolling a three), probability of failure (rolling anything other than a three), number of times die is rolled, and number of successes you want.

Answer 1

P(x) = C(n,x)p^x(1-p)^(n-x)

n = 5

p = 1/6

x = 2

C(n,x)p^x(1-p)^(n-x) = C(5,2)(1/6)^2(1-1/6)^(5-2) = 10 * 1/36 * 125/216 = 625/3888 = .1608

In Excel, you can get this using =BINOMDIST(2,5,1/6,0)