The principle of redundancy is used when system reliability is improved through

Question

The principle of redundancy is used when system reliability is improved through redundant or backup components. A region's government requires that commercial aircraft used for flying in hazardous conditions must have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.0038 . What is the probability that a particular flight will be threatened with the failure of both radios? Describe how the second independent radio increases safety in this case. What is the probability that a particular flight will be threatened with the failure of both radios?

Explanation / Answer

Solution:

If the probability that one of them will fail is 0.0038 then the probability that both will fail at the same time is

0.0038 * 0.0038 = 1.44 * 10^-5 which is equal to 0.00001444
If you round to 3 decimal places, your answer will be 0.000 which doesn't capture the essence of what the data is trying to tell you very well.

while 0.00001444 is very small, it is not 0.

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