Two pumps connect in parallel fail independently of one anot

Two pumps connect 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. The pumping station fails when BOTH pumps fail.

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

Solution

We need to find the union between the failure of the two pumps, where they both fail at the same time.

Step 1: P(pump1 fail)=.10

P(pump2 fail)=.05

Step 2:

P(pump1 and pump2 fail)=.10*.05=.005

Probability that the pumping station will fail on any given day=.005.

Hope this helps! :) Let me know if you have any other questions.