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. [Round your answers to three decimal places, for example: 0.123]

If you randomly select two peanut M&M’s, compute that probability that neither of them are yellow.
If you randomly select two peanut M&M’s, compute that probability that at least one of them is yellow.

P(~yellow) = 1 - P(yellow)

multiply for each draw (assuming that there are enough M&Ms that drawing a few does not affect the probabilities)

1 minus the answer to part A.

To calculate the probability in both scenarios, we need to consider the probability of selecting each color for the first M&M and then adjust the probabilities for the second M&M based on the first selection.

1. Probability that neither of the M&M's are yellow:
To calculate this probability, we need to find the probability of selecting a non-yellow M&M for both the first and second M&M.

First, let's calculate the probability of selecting a non-yellow M&M for the first M&M:
The probability of selecting a non-yellow M&M for the first M&M is 1 minus the probability of selecting a yellow M&M. Therefore, the probability of selecting a non-yellow M&M for the first M&M can be calculated as:
1 - 0.15 (probability of selecting yellow M&M) = 0.85.

For the second M&M, since one M&M has already been selected, we need to adjust the probabilities. After selecting a non-yellow M&M for the first one, the number of non-yellow M&M's remaining has decreased by 1, and the total number of M&M's remaining has decreased by 1 as well.

Therefore, the probability of selecting a non-yellow M&M for the second M&M, given that the first is non-yellow, is:
(number of remaining non-yellow M&M's) / (total number of remaining M&M's)

To calculate this, we subtract the number of yellow M&M's from the original count of M&M's:
Total M&M's - yellow M&M's = 100% - 15% = 85%

So, the probability of selecting a non-yellow M&M for the second M&M, given that the first is non-yellow, is 85%.

Now, to find the probability that neither of the two M&M's are yellow, we multiply the probabilities of the two selections:
0.85 (probability of selecting a non-yellow M&M for the first M&M) * 0.85 (probability of selecting a non-yellow M&M for the second M&M) = 0.7225.

Therefore, the probability that neither of the two peanut M&M's are yellow is approximately 0.723.

2. Probability that at least one of the M&M's is yellow:
To calculate this probability, we need to find the complement of neither M&M being yellow, i.e., we calculate the probability of at least one M&M being yellow and then subtract it from 1.

The probability of at least one M&M being yellow is the complement of neither M&M being yellow. Therefore, the probability of at least one M&M being yellow can be calculated as:
1 - 0.723 (probability that neither M&M is yellow) = 0.277.

Therefore, the probability that at least one of the two peanut M&M's is yellow is approximately 0.277.