1. ## Probability question

Two pumps connected in parallel fail independently of one another on any given day.The probability that only the older pump will fail is .10 and the probability that only the newer pump will fail is.05.What is the probability that the pumping system will fail on any given day(which happens if both pump fails)..

I just thought it was easy.

P(O) = .10
P(N)=.05

so P(O intersection N) is .10*.05 since they're independent events = probability that the machine fails on any given day but it gives me the wong answer.

2. Hello, NidhiS!

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)?
Like you, I thought it was easy . . . then I read it again.

Let $p$ = prob. that the old pump fails.
. . Then $1-p$ = prob. that the old pump works.

Let $q$ = prob. that the new pump fails.
. . Then $1-q$ = prob. that the new pump works.

"The probability that only the old pump will fail is 0.10."
. . This means: the old pump fails and the new pump works.
. . So we have: . $p(1-q) \:=\:\tfrac{1}{10}\;\;{\color{blue}[1]}$

"The probability that only the new pump will fail is 0.05."
. . This means: the new pump fails and the old pump works.
. . So we have: . $q(1-p) \:=\:\tfrac{1}{20}\;\;{\color{blue}[2]}$

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

3. Thanks,that really helps