Question

A manufacturing machine has a 5% defect rate.

If 6 items are chosen at random, what is the probability that at least one will have a defect?

Answer 1

To find the probability that at least one item will have a defect out of a sample of 6 items with a 5% defect rate, use the complement rule. The probability is approximately 26.5%.

Step-by-step explanation:

To find the probability that at least one item will have a defect out of a sample of 6 items, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.

First, we need to find the probability that none of the items will have a defect.

Since the defect rate is 5%, the probability of an item not having a defect is 1 - 0.05

= 0.95.

Since the items are chosen at random, the probability of all 6 items not having a defect is (0.95)^6 ≈ 0.735.

Now, we can use the complement rule to find the probability that at least one item will have a defect. 1 - 0.735

= 0.265, or approximately 26.5%.

Therefore, the probability that at least one item will have a defect is 0.265, or 26.5%.