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

The probability that the system functions, requiring both A and B to function, is calculated using the formula for the probability of either event occurring. By rearranging and substituting the given probabilities, we find that the probability the system functions is 0.94.

Step-by-step explanation:

Calculation of System Functionality Probability

To determine the probability that the system functions, we need to find the joint probability that both A and B function, denoted as P(A AND B). Given that the probability A functions is 0.98, and B functions is 0.95, we use the given that the probability either A or B functions (which includes the case where both function) is 0.99.

We start with the formula for the probability that either A or B functions, which is:

P(A OR B) = P(A) + P(B) − P(A AND B)

.

We can rearrange this to solve for P(A AND B):

P(A AND B) = P(A) + P(B) − P(A OR B)

.

Substituting the given probabilities, we get:

P(A AND B) = 0.98 + 0.95 − 0.99 = 0.94

.

Therefore, the probability that the system functions, which requires both A and B to function, is 0.94.

Answer 2

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%.