Among 6072 cases of heart pacemaker malfunctions, 356 were found to be caused by

Question

Among 6072 cases of heart pacemaker malfunctions, 356 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in 3 different pacemakers randomly selected from this batch of 6072 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted? The probability is This procedure is (Round to three decimal places as needed.) to result in the entire batch being accepted.

Explanation / Answer

there are 356 pacemaker caused by firmware

total = 6072

probability that entire batch is selected
=P(first one is selected )*P(second one is selected )*P(third one is selected)

=(1-356/6072)*(1-355/6071)*(1-354/6070)
= 0.8346338

= 0.835

this procedure is certain to result in the entire batch

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