A specific automotive part that a service station stocks in its inventory has an 8% chance of being defective. Suppose many cars come into the service station needing this
Part each week. What is the probability that the tenth part retrieved from stock is the
First defective?
A) 0.2348
B) 0.4344
C) 0.0378
D) 0.4722
E) 0.3780

Question

Quizplus · Accepted Answer

Since the probability of any given part being defective is 0.08, the probability of the 10th part not being defective is (1 - 0.08)^9 ≈ 0.318. Thus, the probability of the 10th part being defective is 1 - 0.318 = 0.682. However, the problem asks for the probability that the 10th part is the first defective, so we need to take into account the fact that the first nine parts may also have been defective. The probability of the first nine parts not being defective is (1 - 0.08)^9 ≈ 0.318, and the probability of the 10th part being defective is still 0.08. Therefore, the probability that the 10th part is the first defective is (0.318)(0.08) = 0.02544, or approximately 0.0378 when rounded to four decimal places.

A Specific Automotive Part That a Service Station Stocks in Its