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Question
A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96. What is the probability that neither is available when needed?
Solution
A be the event of availability of a fire B be the event of a fire engine when needed.
Availability of a second fire engine when needed.
Given P(A) = 0.96
P(B) = 0.96
Then `bar"A"` is the event of non-availability of the first fire engine and `bar"B"` is the event of non-availability of second fire engine when needed.
`"P"(bar"A") = 1 - "P"("A")`
= 1 – 0.96
= 0.04
Also P(B) = 0.04
P(A’ ∩ B’) = P(A’) P(B’)
= 0.04 × 0.04
= 0.0016
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