A piece of equipment contains six identical items and it is known that three of them...
- A piece of equipment contains six identical items and it is known that three of them are defective. The items are tested one after the other until the three defective items are found.
(a) What is the probability that the testing process is stopped on the (i) third
test (ii) fourth test.
(b) If the process is stopped on the fourth test, what is the probability that the first item is not defective.
Homework Answers
a) i) P(stopped on third test) = 3/6 * 2/5 * 1/4 = 0.05
ii) P(stopped on fourth test) = 3/6 * 3/5 * 2/4 * 1/3 + 3/6 * 3/5 * 2/4 * 1/3 + 3/6 * 2/5 * 3/4 * 1/3 = 0.15
B) P(first item is not defective | stopped on the fourth test) = P(first item is not defective and stopped on fourth test)/P(stopped on the fourth test) = (3/6 * 3/5 * 2/4 * 1/3)/0.15 = 0.3333
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