According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green.

Compute the probability that two randomly selected peanut M&M’s are both blue.
If you randomly select two peanut M&M’s, compute that probability that neither of them are red.
If you randomly select two peanut M&M’s, compute that probability that at least one of them is red.

3 answers

The probabilities of colors of each pill are independent.

Let m[n] = C, be the event that the [n]th pill is a color (C). eg: P(m1=Blue) = 0.12

(1)
P(m1=Blue and m2=Blue) = P(m1=Blue) P(m2=Blue)

(2)
P(m1<>Red and m2<>Red) =
(1-P(m1=Red))(1-P(m2=Red))

(3)
P(m1=Red or m2=Red) = P(m1=Red) + P(m2=Red) - P(m1=Red) P(m2=Red)

12%

1) .0529