what is the probability that the circuit operates

Question

The following circuit operates only if there is a path functional devices from left to
right. The probability that each device functions is: P(A)=0.995; P(B)=0.99;
P(C)=P(D)=P(E)=0.95; P(F)=P(G)=0.90; P(H)=0.98 and P(I) = 0.90. Assume all
devices function independently, what is the probability that the circuit operates?

 

 

 

 

Answer 1

Since all the devices are independent, the answer is the product of the probabilities that each one works.

 

P(Circuit Works) = P(A)×…×P(I)

 

= (0.995)(0.99)(0.95)³(0.90)²(0.98)(0.90) ≈ 0.603 = 60.3%