Question

The probability to get SBA PPP loan for some group of small businesses is 0.8. Of 6 small businesses randomly selected, what is the probability that exactly 2 will be rejected

Answer 1

Using the binomial distribution, it is found that there is a 0.2458 = 24.58% probability that exactly 2 will be rejected.

For each business requesting a loan, there are only two possible outcomes, either it is rejected, or it is not. The probability of each business getting a loan is independent of any other business, hence, the binomial distribution is used to solve this question.

What is the binomial distribution formula?

The formula is:

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

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

The parameters are:

• x is the number of successes.

• n is the number of trials.

• p is the probability of a success on a single trial.

In this problem:

• The probability to get SBA PPP loan for some group of small businesses is 0.8, hence the probability it is rejected is $p = 1 - 0.8 = 0.2$.

• 6 small businesses are randomly selected, hence $n = 6$.

The probability that exactly 2 will be rejected is P(X = 2), hence:

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

$P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458$

0.2458 = 24.58% probability that exactly 2 will be rejected.

You can learn more about the binomial distribution at https://brainly.com/question/24863377