Question

A survey showed that 70% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 7 adults are randomly selected, find the probability that exactly 2 of them need correction for their eyesight.

Answer 1

0.0250047

Explanation:

Given that :

Proportion who need correction glasses = 70%

Number of trials = 7

Probability that exactly 2 needs correction glasses :

Using a binomial probability formula :

P(success) = p = proportion who need glasses = 0.7

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

P(x = 2) = 7C2 * 0.7^2 * 0.3^(7 - 2)

P(x = 2) = 7C2 * 0.7^2 * 0.3^5

P(x = 2) = 21 * 0.49 * 0.00243

P(x = 2) = 0.0250047