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.

Question

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]

Compute the probability that a randomly selected peanut M&M is not orange.

Compute the probability that a randomly selected peanut M&M is green or yellow.

Compute the probability that two randomly selected peanut M&M’s are both brown.

If you randomly select two peanut M&M’s, compute that probability that neither of them are blue.

If you randomly select two peanut M&M’s, compute that probability that at least one of them is blue.

Answer 1

Compute the probability that a randomly selected peanut M&M is not orange.

23% are orange, so 77% are not orange, which equates to a 0.77 probability.

Compute the probability that a randomly selected peanut M&M is green or yellow.

15% are green and 15% are yellow, so 30% are either green or yellow, which equates to 0.30 probability.

Compute the probability that two randomly selected peanut M&M’s are both brown.

Assuming there is a large enough amount of M and Ms such that each selection can be considered independent. Probability of each selection being brown is 0.12, so probability of both being brown is 0.12 * 0.12 = 0.0144.

If you randomly select two peanut M&M’s, compute that probability that neither of them are blue.

Probability of being blue is 0.23, so probability of not being blue is 0.77. Probability of both not being blue is 0.77 * 0.77 = 0.5929.

If you randomly select two peanut M&M’s, compute that probability that at least one of them is blue.

So either have 1 Blue or 2 Blues.

Probability of blue is 0.23, so probability of both selections being blue is 0.23 * 0.23 = 0.0529

Probability 1st being blue and second one not being blue = 0.23 * 0.77 = 0.1771

Probability 2nd being blue and 1st not being blue = 0.23 * 0.77 = 0.1771

Probability of any of these events occurring is 0.0529 + 0.1771 + 0.1771 = 0.4071