A local manufacturing company has a defect rate of 6% for its facility.

What is the probability that when five items are selected from the production line, AT LEAST ONE of them is defective?

1 answer

To find the probability that at least one of the five selected items is defective, we can find the probability that none of the five items are defective and subtract it from 1.

The probability of an item being defective is 6% or 0.06.
The probability of an item not being defective is 1 - 0.06 = 0.94.

The probability that none of the five items are defective is calculated as follows:
P(no defective items) = P(item 1 not defective) * P(item 2 not defective) * P(item 3 not defective) * P(item 4 not defective) * P(item 5 not defective)

P(no defective items) = 0.94 * 0.94 * 0.94 * 0.94 * 0.94

P(no defective items) ≈ 0.8305

Therefore, the probability that at least one of the five selected items is defective is:
P(at least one defective item) = 1 - P(no defective items)

P(at least one defective item) ≈ 1 - 0.8305 ≈ 0.1695

The probability that at least one of the five selected items is defective is approximately 0.1695, or 16.95%.