Question

An electrical device has two components, A and B. Each component can be "good" or can be in a "shorted" or "open-mode" failure state. Let's assume that component A has probability .6 or being good and probability .2 of being in each of the failure states, and that component B has probability .7 of being good, .2 of "open" failure, and .1 for "shorted" failure. Furthermore, we assume the two components function independently.

Current can pass through a device if it is "good" or if it is in the "shorted" failure state.

a) whats the probability that at least one of the components is shorted?

b)whats the probability that neither is good?

c) if the two components are wired in series, what then is the probability that current can pass through?

d)if they are wired in parallel, whats the probability that current can pass through?

Answer 1

a) probability that at least one of the components is shorted =1-P(neither is Shorted)

=1-P(A is not shorted)*P(product B is not shorted) =0.8*0.9=0.28

b)

probability that neither is good =P(A is not good)*P(product B is not good) =0.4*0.3=0.12

c)

probability that current can pass through =P(A is not open)*P(B is not open)=0.8*0.8=0.64

d)

probability that current can pass through =1-P(both are open)=1-0.2*0.2=0.96

Answer 2