Homework Answers
(a)
Given, the first one was defective, number of defective in remaining sample of 299 is 7.
Probability that the second one is defective = 7/299 = 0.02341137
(b)
Probability that the first one is defective = 8/300
Now, if the first one is defective, number of remaining defective samples is 7 out of remaining 299 samples
Probability that the second one is defective = 7/299
Probability that both are defective = Probability that the first one is defective * Probability that the second one is defective
= (8 / 300) * (7 / 299)
= 0.0006243032
(c)
Initial number of acceptable samples = 300 -8 = 292
Probability that the first one is acceptable = 292/300
Now, if the first one is acceptable, number of remaining acceptable samples is 291 out of remaining 299 samples
Probability that the second one is acceptable = 291 / 299
Probability that both are defective = Probability that the first one is defective * Probability that the second one is defective
= ( 292/300) * (291 / 299)
= 0.947291
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