Given: Let A and B be two fire extinguishing engines .
The probability of availability of each of the two fire extinguishing engines is given i.e.,
P(A) = 0.95 and P(B) = 0.95
⇒
P(
¯
A
) = 0.05 and P(
¯
B
) = 0.05
To Find:
(i) The probability that neither of them is available when needed
Here, P(not A and not B) = P(
¯
A
∩
¯
B
)
= P(
¯
A
) x P(
¯
B
)
= 0.05 x 0.05
= 0.0025 =
1
100
Therefore, The probability that neither of them is available when needed is
1
400
(ii) an engine is available when needed
Here, P(A and not B or B and not A) = P( A ∩
¯
B
) + P(B ∩
¯
A
)
=
19
200
Therefore, The probability that an engine is available when needed is
19
200
