Among 9774 cases of heart pacemaker malfunctions, 521 were found to be caused by

Question

Among 9774 cases of heart pacemaker malfunctions, 521 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 9774 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 [[ unlikely /likely /certain ]]to result in the entire batch being accepted.
(Round to three decimal places as needed.)

Explanation / Answer

P (peacemaker malfunctions caused by firmware) = 521/9774 = 0.053
X ~ Binomial Distribution with parameters n = 3, p = 1–0.053 = 0.947
P (the firmware in the entire batch will be accepted)
= P (X = 3)
=ncxpxqn-x
=3c3 (0.947)3(1-0.947)3-3
=1*0.8492*1
= 0.8492

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