The shell of the snail Cepaea nemoralis can be yellow, pink, or brown. Suppose t

Question

The shell of the snail Cepaea nemoralis can be yellow, pink, or brown. Suppose that a very large natural population of this species consists of 27% yellow, 39% pink, and 34% brown individuals. If you randomly sample 2 snails from this population, what is the probability that

(a) both are yellow?

(b) neither is yellow?

(c) one is yellow and one is not? [Hint: when taking a small sample from a very large population, sampling without replacement is essentially the same as sampling with replacement since removing a few individuals does not significantly alter the makeup of the population.]

(show full solution)

Explanation / Answer

Probability of yellow species P(Y) = 0.27

Probability of pink species P(P) = 0.39

Probability of brown species P(B) = 0.34

(A)

Required probability = P(Y)^2 = 0.27^2 = 0.0729

(B)

Probability of not yellow = 1-P(Y) = 1-0.27 = 0.73

Required probability = 0.73^2 = 0.5329

(C)

Required probability = P(Y) * (1-P(Y)) = 0.27*0.73 = 0.1971

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