Question

Assume that when an adult is randomly​ selected, the probability that they do not require vision correction is 23​%. If 6 adults are randomly​ selected, find the probability that exactly 2 of them do not require a vision correction.

Answer 1

Answer:

 P(X = 2) = 0.27894

Step-by-step explanation:

Given:

- The probability that no vision correction is required p = 0.23

- No. adults are randomly selected n = 6

Find:

- P ( Exactly 2 dont require vision correction)

Solution:

- We will declare a random variable X is the umber of adults out of 6 that do  not require vision correction. X follows a Binomial distribution:

                                    X~ B ( 6 , 0.23 )

- The probability required is P ( X = 2 )

- Using the pmf of binomial distribution we have:

                           P(X = 2) = 6C2 * (0.23)^2 * (0.77)^4

                           P(X = 2) = 15 * 0.0529 * 0.35153041

                           P(X = 2) = 0.27894