Question

Among 9976 cases of heart pacemaker malfunctions, 465 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 9976 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?

Answer 1

Solution:

The given information is as follows:

Total number of cases of pacemaker malfunctions = 9976

Number of pacemaker malfunctions caused by firmware = 465

The firmware is tested in 3 different pacemakers selected randomly and the batch is accepted if there are no failure&

The probability that malfunction is caused by firmware = 465 / 9976 = 0.0466

So, the probability that a malfunction is not caused by firmware =1-0.0466= 0.9534‬

The batch will be accepted if all the 3 pacemakers in the sample do not fail due to firmware malfunction. So, the probability that the entire batch will be accepted is computed as shown below:

P]Batch is accepted] = 0.9534‬* 0.9534‬ * 0.9534‬ = 0.8666

Thus, there are approximately 86.66% chances that the entire batch will be accepted.

The chance of acceptance of the batch is quite high, therefore, the procedure is likely to result in acceptance of entire batch.