According to a recent survey, 81 percent of adults in a certain state have graduated from high school. If 15 adults from the state are selected at random, what is the probability that 5 of them have not graduated from high school?

0.090401

Step-by-step explanation:

Given that:

Probability of graduate = 81% = 0.81

P( not graduate) = p = (1 - 0.81) = 0.19

1 - p = 0.81

Using binomial distribution :

P(x = x) = nCx * p^x * 1-p^(n-x)

n = 15 ; x =5

P(x = 5) = 15C5 * 0.19^5 * 0.81^(15 - 5)

P(x = 5) = 15C5 * 0.19^5 * 0.81^10

P(x = 5) = 3003 * 0.0002476099 * 0.12157665459056928801

P(x = 5) = 0.090401

If you would like to find the simplified form, you can do this using the following steps:

(2x - 3x^2) / (5x^3) = (x(2 - 3x)) / (x(5x^2)) = (2 - 3x) / (5x^2) if x != 0

The correct result would be (2 - 3x) / (5x^2) if x != 0.