Need help on this Binomial Distribution question Math 1040 6

6) (10 points) [Binomial Distribution] Assume that in a typical bag of M&M;\'s, the percent of each colors are 24% blue, 14% brown, 16% green, 20% orange, 13% red and 13% yellow. a. What is the probability that out of a random sample of 10 M&M;\'s, there are exactly 3 blue M&M;\'s? b. What is the probability that out of a random sample of 10 M&M;\'s, there are more than 3 green M&M;\'s?

Solution

a)

using binomial distribution

P(X =3) = 10C3 * 0.24^3 * 0.76^7 = 0.2430

b)

P(X>3) = 1- P(X<3)

= 1 - P(X=0) + P(X=1) + P(X=2) + P(X=3)

= 1 - 0.76^10 + 10 * 0.24 * 0.76^9 + 10C2 * 0.24^2 * 0.76^8 + 0.2430

= 0.2012