Question

A child is observing squirrels in the park and notices that some are black and some are gray. For the next five squirrels she sees, she counts X = the number of black squirrels. Suppose 20% of squirrels are black. What is the probability that she will see exactly two black squirrels out of the five?

Answer 1

Answer:

20.48% probability that she will see exactly two black squirrels out of the five

Step-by-step explanation:

For each squirrel, there are only two possible outcomes. Either it is black, or it is not. The probability of a squirrel being black is independent of other squirrels. So we use the binomial probability distribition to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

20% of squirrels are black.

This means that $p = 0.2$

What is the probability that she will see exactly two black squirrels out of the five?

This is P(X = 2) when n = 5. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{5,2}.(0.2)^{2}.(0.8)^{3} = 0.2048$

20.48% probability that she will see exactly two black squirrels out of the five