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A safety system relies on two measuring instruments, X and Y, which operate independently. Over a...

A safety system relies on two measuring instruments, X and Y, which operate independently. Over a five year period there is a 1 in 70 chance that X will fail and a 1 in 130 chance that Y will fail. What is the probability that either or both of the two instruments will fail during the same five year period? Express your answer as a percentage to 3 decimal places. The probability of either or both devices failing is:

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Answer #1

Over a five year period there is a 1 in 70 chance that X will fail and a 1 in 130 chance that Y will fail,

so, if P(X)= probability that X will fail = 1/70

P(Y)= 1/130

both of these instruments operate independent, so

Probability that both will fail during the same five year period =

probability of either or both devices failing=

So, probability of either or both failing =0.02186813

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