Suppose that 90% of bolts and 85% of nails meet specifications. One bolt and one nail are chosen independently.
a. What is the probability that both meet specifications?
b. What is the probability that neither meets specifications?
c. What is the probability that at least one of them meets specifications?
Let Arepresent the event that the bolt meets specifications, and let B represent the event that the nail meet specifications. Then P(A) = 0.9 and P(B) = 0.85.
(a) P(A ? B) = P(A)P(B) = (0.9)(0.85) = 0.765.
(b) 
= (1?0.9)(1 ? 0.85) = 0.015.
(c) P(A 
B)=P(A) + P(B) ? P(A ? B)
=P(A) + P(B) ? P(A)P(B)
=0.9 + 0.85 ? (0.9)(0.85)
=0.985
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