## Related questions with answers

Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device (based on data from "Pacemaker and ICD Generator Malfunctions," by Maisel et al. , Journal of the American Medical Association, Vol. 295 , No. 16). If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and th e enti re batch is accepted if there are no fa ilures, 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?

Solution

VerifiedDEFINITIONS

Two events are $\textbf{independent}$, if the probability that one event occurs in no way affects the probability of the other event occurring.

$\textbf{General multiplication rule}$:

$P(A\text{ and }B)=P(A\cap B)=P(A)\times P(B|A)=P(B)\times P(A|B)$

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