Question

20 Items were randomly selected from a large inventory. If 10% of the items in the inventory are made in Asia,

1. What is the probability that exactly 2 of the 20 items selected are made in Asia? (2 Points)

2. What is the probability that at most 2 of the 20 items selected are made in Asia? (2 Points)          

Answer 1

n = 20

p = 0.1

It is a binomial distribution.

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

a) P(X = 2) = 20C2 * (0.1)^2 * (0.9)^18 = 0.2852

b) P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

                  = 20C0 * (0.1)^0 * (0.9)^20 + 20C1 * (0.1)^1 * (0.9)^19 + 20C2 * (0.1)^2 * (0.9)^18

                  = 0.6769