Suppose that 90% of bolts and 85% of nails meet specifications. One bolt and one nail are chosen independently. What is the probability that both meet specifications? What is the probability that neither meets specifications? What is the probability that at least one of them meets specifications?

76.5% probability that both meet specifications.

1.5% probability that neither meets specifications

98.5% probability that at least one of them meets specifications

Step-by-step explanation:

We have these following probabilities:

A 90% probability that a bolts meets specifications

A 85% probability that a nail meets specifications.

What is the probability that both meet specifications?

We multiply both probabilities:

0.9*0.85 = 0.765

76.5% probability that both meet specifications.

What is the probability that neither meets specifications?

A 10% probability that a bolts does not meet specifications

A 15% probability that a nail does not meet specifications.

0.1*0.15 = 0.015

1.5% probability that neither meets specifications

What is the probability that at least one of them meets specifications?

Either neither meets specifications, or at least one of them does. The sum of these probabilities is 100%.

From the second question, 1.5% probability that neither meets specifications.

So 100-1.5 = 98.5% probability that at least one of them meets specifications