Question

. A system contains two components, A and B. The system will function only if both components function. The probability that A functions is 0.98, the probability that B functions is 0.95, and the probability that either A or B functions is 0.99. What is the probability that the system functions?

Answer 1

Answer:

0.94

Step-by-step explanation:

System will function if both components function, so,

P(system function)=P(A∩B)=?

P(A∩B)=P(A)+P(B)-P(A∪B)

We are given that P(A)=0.98, P(B)=0.95 and P(A or B)=P(A∪B)=0.99.

P(A∩B)=0.98+0.95-0.99=1.93-0.99=0.94

P(system function)=P(A∩B)=0.94.

Thus, the probability that the system functions is 0.94 or 94%.