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.
[tex]\Rightarrow P(A \cap B) = P(A) \times P(B)[/tex]
[tex]P(A \cap B) = 0.10 \times 0.15\\\Rightarrow P(A \cap B) = 0.015[/tex]
The probability that the system will fail i.e. both the pumps will fail is 0.015.
