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.

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