Question

Assume that when an adult is randomly selected, the probability that they do not require vision correction is 18%. If 8 adults are randomly selected, find the probability that exactly 2 of them do not require a vision correction. If 8 adults are randomly selected, the probability that exactly 2 of them do not require a vision correction is (Round to three decimal places as needed.)

Answer 1

The probability that exactly 2 out of 8 randomly selected adults do not require vision correction is approximately 0.4554.

Step-by-step explanation:

To find the probability that exactly 2 out of 8 randomly selected adults do not require vision correction, we can use the binomial probability formula. The formula is:

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

Where P(x) is the probability of getting exactly x successes, n is the number of trials, p is the probability of success, and nCx is the number of combinations of n items taken x at a time.

In this case, x = 2, n = 8, and p = 0.18. Plugging these values into the formula:

P(2) = (8C2) * (0.18^2) * ((1-0.18)^(8-2))

= (28) * (0.0324) * (0.4965)

= 0.4554

So, the probability that exactly 2 out of 8 randomly selected adults do not require vision correction is approximately 0.4554.