Question

An incoming lot of silicon wafers is to be inspected for defective ones by an engineer...

An incoming lot of silicon wafers is to be inspected for defective ones by an engineer in a
microchip manufacturing plant. Suppose that in a tray containing 24 wafers 6 are defective. Two
wafers are to be selected randomly for inspection. Find the probabilities of the following events.
a. Neither is defective.
b. At least one of the two is defective.
c. Neither is defective, given that at least one is not defective.
d. Answer answer the same three questions, assuming this time that only 3 among the 24
wafers are defective.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a) P(neither is defective) = 18C2/24C2 = 0.5543

b) P(At least one is defective) = (6C1 * 18C1 + 6C2)/24C2 = 0.4457

c) P(neither is defective | at least one is not defective) = 18C2/(6C1 * 18C1 + 18C2)

                                                                                      = 0.5862

d)i) P(neither is defective) = 21C2/24C2 = 0.7609

ii) P(At least one is defective) = (3C1 * 21C1 + 3C2)/24C2 = 0.2391

iii) P(neither is defective | at least one is not defective) = 21C2/(3C1 * 21C1 + 21C2) = 0.7692

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