Multiple choice: Probability

Question

A particular system is composed of three machine. A, B, and C. The entire system will work as long as any one (or more than one of the three machines works. (The system is WITH backup).

P(A works) = 0.60

P(B works) = 0.70

P(C works) = 0.85

Round to the fourth digit beyond the decimal point (if it goes that far)

P(the entire system works)

Answer 1

Assuming that the machines work or fail independently of one another, we can compute P(system fails) as follows:

P(system fails) = P(A fails & B fails & C fails) = (1 - 0.6) * (1 - 0.7) * (1 - 0.85)

= 0.4 * 0.3 * 0.15 = 0.018

Having calculated this, we can find the probability that the system works by subtracting from 1:

P(system works) = 1 - P(system fails) = 0.982