Question

Suppose that 88% of bolts and 83% 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.)

Answer 1

0.9796

Explanation:

Given that 88%of bolts and 83% of nails meet specifications.

This implies that for a randomly selected bowl the prob that it meets specifications = P(A) = 0.88

Similarly, for a randomly selected bolt, it meets specifications is P(B) = 0.83

We know that bolt and nail are independent of each other.

Hence
`P(A \bigcap B) = P(A)P(B)\\\\=0.88*0.83=0.7304`

Required probability = Probability that atleast one of them meets specifications)

`= P(AUB)\\=P(A)+P(B)-P(A \bigcap B)\\=0.88+0.83-0.7304\\=1.71-0.7304\\=0.9796`