Probability: machines will work

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

The only way the system will not work is if all machines A, B and C do not work, therefore:

P(the entire system works) = 1 - P(the three machines don't work)

P(the entire system works) = 1 - [(1 - 0.60) * (1 - 0.70) * (1 - 0.85)]

P(the entire system works) = 1 - 0.018

P(the entire system works) = 0.982