M&Ms; are blended in a ratio of 11 percent brown. 9 percent yellow. 9 percent re

Question

M&Ms; are blended in a ratio of 11 percent brown. 9 percent yellow. 9 percent red: 17 percent blue. 16 percent orange, and 38 percent green. Suppose you choose a sample of two M&Ms; at random from a bag. How many elements are there in the sample space, assuming the order in which the M&Ms; are drawn matters? What is the probability that both are brown? What is the probability that both are blue? What is the probability that both are green? What is the probability that the first M&M; is brown and the second is green?

Explanation / Answer

1.
To find the elements of the sample space, we look at the possible outcomes and count them. Here, since we are choosing two M&M's and there are 6 different colors of M&M's, there are 6*6 = 36 elements in the sample space.

2.
Assuming replacement of M&M's after picking and thus independent events on each pick, the probability that both are brown will be:
Pr(both brown) = 0.13 * 0.13 = 0.0169

3.
Assuming replacement of M&M's after picking and thus independent events on each pick, the probability that both are blue will be:
Pr(both blue) = 0.24 * 0.24 = 0.0576

4.
Assuming replacement of M&M's after picking and thus independent events on each pick, the probability that both are green will be:
Pr(both green) = 0.16 * 0.16 = 0.0256

5.
P(brown then green) = 0.13 * 0.16 = 0.0208
P(green then brown) = 0.16 * 0.13 = 0.0208
Summing these gives P(one green; one brown) = 0.0416

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