Question

We have a box with 9 green M&M's and 4 white M&M's. Draw 3 M&M's from the box without replacement and record their colors (Do not eat them!) and then put them back in the box. Repeat this procedure 20 times. Let X denote the number of times that the procedure (drawing 3 M&M's) resulted in exactly 3 green M&M's out of the 20 repetitions. What is the probability that at least 2 of the procedures resulted in exactly 3 green M&M’s? Round your answer to 3 decimal places.

Answer 1

Total M&M's = 9 + 4 = 13

P(getting 3 green M&M's) = 9C3 / 13C3 = 84 / 286 = 0.294

Now this is a binomial distribution with p = 0.294 and n = 20

P(X = x) = 20Cx * 0.294^x * (1 - 0.294)^20-x

P(X > 2) = 1 - P(X < 2)

              = 1 - (P(X = 0) + P(X = 1))

              = 1 - (20C0 * 0.294⁰ * 0.704²⁰ + 20C1 * 0.294¹ * 0.704¹⁹)

              = 1 - 0.009

              = 0.991 (ans)