Consider the following diagram of a mechanical system which

Consider the following diagram of a mechanical system, which shows the component numbers and the probabilities of the system components operating properly. What is the probability that the entire system operates if at least one ‘operating’ path must exist from left to right in order for the system to operate? (This figure is called a block diagram.) Assume that all components operate independently

Solution

Here,

P(working) = (0.97 or 0.95) and (0.90 or 0.96 or 0.85) and (0.99 or 0.98)

= (0.97 + 0.95 - 0.97*0.95)*(0.90 + 0.96 + 0.85 - 0.90*0.96 - 0.96*0.85 - 0.90*0.85 + 0.90*0.96*0.85)*(0.99 + 0.98 - 0.99*0.98)

= 0.99770132 [ANSWER]