Hello, NidhiS!

Like you, I thought it was easy . . . then I read it again.Two pumps connected in parallel fail independently of one another on any given day.

The probability that only the older pump will fail is 0.10

and the probability that only the newer pump will fail is 0.05.

What is the probability that the pumping system will fail on any given day

(which happens if both pump fails)?

Let = prob. that the old pump fails.

. . Then = prob. that the old pump works.

Let = prob. that the new pump fails.

. . Then = prob. that the new pump works.

"The probability thatthe old pump will fail is 0.10."only

. . This means: the old pump failsandthe new pump works.

. . So we have: .

"The probability thatthe new pump will fail is 0.05."only

. . This means: the new pump failsandthe old pump works.

. . So we have: .

Then, between [1] and [2], we must find (the prob. that both fail).