Let X1 X2 X3 X4 X5 and X6 denote the numbers of blue brown g

Let X1, X2, X3, X4, X5 and X6 denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. According to the M&M website, the color proportions are p1 = 0.24, p2 = 0.13, p3 = 0.16, p4 = 0.2, p5 = 0.13, and p6 = 0.14.

(a) If n = 12, what is the probability that there are exactly two M&M’s of each color?

(b) For n = 20, what is the probability that there are at most 5 orange candies? (Hint: Treat an orange candy as a “success” and any other color as “failure”)

(c) In a sample of 20 M&M’s, what is the probability that the total number of candies that are blue, green or orange is at least 10?

Solution