Answer :
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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
20% of squirrels are black.
This means that [tex]p = 0.2[/tex]
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
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.2)^{2}.(0.8)^{3} = 0.2048[/tex]
20.48% probability that she will see exactly two black squirrels out of the five