A system contains two components, A and B. The system will function so long as either A or B functions. The probability that A functions is 0.95, the probability that B functions is 0.90, and the probability that both function is 0.88. What is the probability that the system functions?

Solution :

Step 1 of 1

Let A and B be the two components.

Let A be the probability function is

P(A) = 0.95

Let B be the probability function is

P(B) = 0.90 and

The probability both function is 0.88

Here both function is A and B.

Therefore

Our goal is to find :

a). What is the probability that the system function?

a).

Now we need to find the probability that the system function.

The formula of is

We know that ,and .

Substitute the all values in the above equation.

Therefore the probability that the system function is 0.97