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Among 9696 cases of heart pacemaker malfunctions, 451 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 9696 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?

User Zorzella
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Final answer:

To find the probability that the firmware in the entire batch will be accepted, calculate the probability of no failures in the 3 randomly selected pacemakers. Whether the procedure is likely to result in the entire batch being accepted depends on the calculated probability.

Step-by-step explanation:

To find the probability that the firmware in the entire batch will be accepted, we need to calculate the probability of no failures in the 3 randomly selected pacemakers.

Since 451 out of 9696 pacemakers were found to be caused by firmware malfunctions, the probability of a failure due to firmware in one pacemaker is 451/9696. Therefore, the probability of no failures in one pacemaker is 1 - (451/9696).

Since the pacemakers are selected randomly, the probability of no failures in all 3 pacemakers is [(1 - (451/9696))^3]. This probability represents the likelihood that the firmware in the entire batch will be accepted.

Whether this procedure is likely to result in the entire batch being accepted depends on the calculated probability. If the probability is high, it is likely that the entire batch will be accepted. However, if the probability is low, there is a higher chance of failures in the entire batch.

User Vicentedealencar
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