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.

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

To compute the probability in each scenario, we need to understand the concept of probability and how it applies here. Probability is the likelihood of an event happening, and it is calculated by dividing the number of desired outcomes by the total possible outcomes.

First, let's find the probability that two randomly selected peanut M&M's are both blue:

1. Calculate the probability of selecting one blue peanut M&M:
- P(Blue) = 23% = 0.23

2. Since we want to select two blue M&M's, we need to multiply the probability of selecting one blue M&M by itself:
- P(Blue and Blue) = P(Blue) * P(Blue) = 0.23 * 0.23 = 0.0529

Therefore, the probability that two randomly selected peanut M&M's are both blue is 0.0529 or 5.29%.

Now let's compute the probability that neither of the two randomly selected peanut M&M's is red:

1. Calculate the probability of selecting one red peanut M&M:
- P(Red) = 12% = 0.12

2. Since we don't want any red M&M's in the selection, we need to calculate the complementary probability of not selecting red M&M's, which is 1 - P(Red):
- P(Not Red) = 1 - P(Red) = 1 - 0.12 = 0.88

3. To find the probability that neither of the two M&M's is red, we multiply the probability of not selecting red by itself since we are selecting two M&M's:
- P(Not Red and Not Red) = P(Not Red) * P(Not Red) = 0.88 * 0.88 = 0.7744

Therefore, the probability that neither of the two randomly selected peanut M&M's is red is 0.7744 or 77.44%.

Now let's find the probability that at least one of the two randomly selected peanut M&M's is red:

1. Calculate the probability of selecting one red peanut M&M:
- P(Red) = 12% = 0.12

2. We want to find the probability that at least one of the selected M&M's is red, which means we need to calculate the complementary probability of both M&M's not being red:
- P(Not Red and Not Red) = P(Not Red) * P(Not Red) = 0.88 * 0.88 = 0.7744

3. To find the probability that at least one of the M&M's is red, we subtract the probability of both M&M's not being red from 1:
- P(At least one Red) = 1 - P(Not Red and Not Red) = 1 - 0.7744 = 0.2256

Therefore, the probability that at least one of the two randomly selected peanut M&M's is red is 0.2256 or 22.56%.