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Assume a cardiovascular surgeon has implanted 10 pacemakers in his patients from a new batch of...

Assume a cardiovascular surgeon has implanted 10 pacemakers in his patients from a new batch of pacemakers that have been found to have a defect that causes them to stop working. If each pacemaker has a 10% chance that it will stop working, what is the probability that all the patients’ pacemakers will work the way they are supposed to?

Math   Statistics-And-Probability   
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Answer #1

Given that each pacemaker has a 10% chance that it will stop workin, the probability that a randomly selected pacemaker will stop working, p=0.10

We have n=10 pacemakers. Let X be the number of pacemakers out of this n=10 pacemakers which have stopped working. X is a random varfiable which has a Binomial distribution with number of trials n=10and success probability (that is the probability of failure) p=0.10

The probability that X=x pacemakers have failed is given by

The probability that all the patients’ pacemakers will work the way they are supposed to is the same as the probability that X=0 pacemakers have failed and is given by

the probability that all the patients’ pacemakers will work the way they are supposed to is 0.3487

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