Question

The manufacturing sector contributes 17% of Canada's gross domestic product. A customer orders 50 components from a factory that has a 99% quality production rate (99% of the products are defect-free). Find the probability that:

a) none of the components in the order are defective,

b) there is at least one defective product in the order.

c) There are at least two defective products in the order.

Answer 1

a)
Here, n = 50, p = 0.01, (1 - p) = 0.99 and x = 0
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 0)
P(X = 0) = 50C0 * 0.01^0 * 0.99^50
P(X = 0) = 0.605

b)
P(X >= 1) = 1 - 0.605 = 0.395

c)
P(X <= 1) = (50C0 * 0.01^0 * 0.99^50) + (50C1 * 0.01^1 * 0.99^49)
P(X <= 1) = 0.605 + 0.3056
P(X <= 1) = 0.9106

P(X >= 2) = 1 - 0.9106 = 0.0894