Final answer:
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%.