Question

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. Among 8834 cases of heart pacemaker malfunctions,504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from the batch of 8834, what is the probability that the firm ware in the entire batch will be accepted? Does the procedure suggest that the entire batch consist of good pacemakers? Why or why not?

Answer 1

Prob of accepting the batch is the prob of all 3 pacemakers passing
Pr(3 passing) = Pr(passing)^3
or
Pr (passing) = 1 - Pr(failing) = 1 - 504/8834