2.19 A mechanical system consists of two subsystems, A and B. A failure of one subsystem places extra load on the other, and will therefore increase the probability of the other failing. Each subsystem is given one preliminary checkout test. Records on 100 of these checkout tests show that subsystem A failed 10 times. Subsystem B alone failed 15 times. Both subsystems A and B failed together 5 times. (a) what is the probability of A failing, given that B has failed? (b) what is the probability that A alone fails?
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We know that both A and B failed together 5 times out of 100 tests. We also know that B failed 15 times in total. So, the probability of A failing given that B has failed can be calculated as the number of times both A and B failed together divided by the total Show more…
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