In a nuclear reactor, the fission process is controlled by inserting into radioa

Question

In a nuclear reactor, the fission process is controlled by inserting into radioactive core a number of special rods whose purpose is to absorb the neutrons emitted by the critical mass and thereby slow down the nuclear chain reaction. When functioning properly, these rods serve as the first-line defense against a core meltdown. Suppose that a particular reactor has 10 of these control rods (in real life there would be more than 100), each operating independently, and each having a 0.8 probability of being properly inserted in the event of an incident. Furthermore, suppose that a meltdown will be prevented if at least half the rods perform satisfactorily. What is the probability that. upon demand, the system will fail?

Explanation / Answer

Ans:

Binomial distribution:

n=10

p=0.8

As,meltdown will be pervented if atleast half(>=5) of the rods perform satisfactroly,so system will fail if less than 5 perform satisfactorily

Hence,P(system fails)=P(k<=4)=BINOMDIST(4,10,0.8,TRUE)=0.0064

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