Please every step in the calculation The shell of the snail

Please every step in the calculation

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.]

Solution

(a) both are yellow?

Probability of sampling yellow snail = 27/100 = 0.27

the probability of two (or more) independent events occurring together can be calculated by multiplying the individual probabilities of the events.

=0.27 x 0.27 = 0.072 = 7.2%

(b) neither is yellow?

Probability of sampling a non yellow snail = 0.39+0.34 =0.73

= 0.73 x 0.73 =0.53 = 53%

(c) one is yellow and one is not?

Probability of sampling yellow snail = 27/100 = 0.27

Probability of sampling a non yellow snail = 0.39+0.34 =0.73