Question

Suppose that 96% of bolts and 91% of nails meet specifications. One bolt and one nail are chosen independently. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

What is the probability that at least one of them meets specifications? (Round the final answer to four decimal places.)

The probability that at least one of them meets specifications is_______

Answer 1

0.9964 is the probability that at least one of them meets specifications.

Explanation:

We are given the following in the question:

B: Bolts meet the specification

N: Nails meet the specification

P(B) = 96% = 0.96

P(N) = 91% = 0.91

One bolt and one nail are chosen independently.

Thus, we can write

`P(B\cap N) = P(B) * P(N) = 0.96* 0.91 = 0.8736`

We have to find the probability that at least one of them meets specifications.

`P(B\cup N) = P(B) + P(N) -P(B\cap N)\\P(B\cup N) =0.96 + 0.91-0.8736\\P(B\cup N) =0.9964`

0.9964 is the probability that at least one of them meets specifications.