Question

A nuclear power plant has two independent safety systems. The probability the first will not operate properly in an emergency P (A) is 0.01, and the probability the second will not operate P (B) in an emergency is 0.03. What is the probability that in an emergency both of the safety systems will not operate?
A. 3
B. 0.03
C. 0.0003
D. None of the choices are correct

Answer 1

Each system is independent of one another, so you multiply the probabilities of failure for each

P(A and B)  = P(A)*P(B)
P(A and B) = 0.01*0.03
P(A and B) = 0.0003

Answer: Choice C

Answer 2

The systems are independent and function independently.  The joint probability in question is 0.01*0.03 = 0.0003.