Question

Items are inspected for flaws by three inspectors. If a flaw is present, each inspector will detect it with a probability of 0.8. The inspectors work independently. If an item has a flaw, what is the probability that at least one inspector detects it?

Could you calculate the probability that at least one inspector detects a flaw in the given example?

Answer 1

To calculate the probability that at least one inspector detects a flaw, calculate the probability that none of them detects a flaw and subtract that from 1. The probability that at least one inspector detects a flaw is 99.2%.

Step-by-step explanation:

To calculate the probability that at least one inspector detects a flaw, we can first calculate the probability that none of the inspectors detects a flaw and then subtract that from 1. Since the inspectors work independently, the probability that none of them detects a flaw is equal to the product of their individual probabilities of not detecting a flaw.

For each inspector, the probability of not detecting a flaw is 1 minus the probability of detecting a flaw, which is 0.2. Therefore, the probability that none of the inspectors detects a flaw is (0.2)(0.2)(0.2) = 0.008. Subtracting this from 1, we find that the probability that at least one inspector detects a flaw is 1 - 0.008 = 0.992, or 99.2%.