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 0.15, and the probability that only the newer pump will fail is 0.10. What is the probability that the pumping system will fail on any given day (which happens if both pumps fail)

Answer 1

Answer:

0.015 is the probability that the pumping system will fail.

Step-by-step explanation:

Given:

There are 2 parallel pumps.

Probability of failing of old pump = 0.10

Probability of failing of new pump = 0.15

Let A be the event that old pump fails, So P(A) be the probability of failing of old pump.

P(A) = 0.10

Let B be the event that newer pump fails, So P(B) be the probability of failing of newer pump.

P(B) = 0.15

It is given that failing of newer and older pumps are independent events.

These events A and B are independent events, happening of one event does not effect the happening of other.

 

$\Rightarrow P(A \cap B) = P(A) \times P(B)$

$P(A \cap B) = 0.10 \times 0.15\\\Rightarrow P(A \cap B) = 0.015$

The probability that the system will fail i.e. both the pumps will fail is 0.015.