Question

1) The manufacturing sector contributes 10% 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: (round to the nearest thousandths when needed) (3 QUESTIONS)

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) To find the probability that none of the components are defective, we can use the binomial probability formula:

P(X = k) = (n C k) * p^k * (1-p)^(n-k)

where n is the number of trials, p is the probability of success on a single trial, and X=k is the event we want to find the probability of.

In this case, n = 50, p = 0.99 (since the factory has a 99% quality production rate), and we want X=0 (none of the components are defective).

P(X=0) = (50 C 0) * 0.99^0 * (1-0.99)^(50-0) = 0.605

Therefore, the probability that none of the components are defective is approximately 0.605.

b) To find the probability that there is at least one defective component, we can use the complement rule and find the probability that all components are non-defective:

P(X ≥ 1) = 1 - P(X=0) = 1 - 0.605 = 0.395

Therefore, the probability that there is at least one defective component is approximately 0.395.

c) To find the probability that there are at least two defective components, we can use the binomial probability formula again:

P(X ≥ 2) = 1 - P(X=0) - P(X=1)

P(X=1) = (50 C 1) * 0.99^1 * (1-0.99)^(50-1) = 0.384

P(X ≥ 2) = 1 - 0.605 - 0.384 = 0.011

Therefore, the probability that there are at least two defective components is approximately 0.011.