Q20 of 42 Page 1283

A town has two fire-extinguishing engines, functioning independently. The probability of availability of each engine when needed is 0.95. What is the probability that

(i) neither of them is available when needed?


(ii) an engine is available when needed?


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() = 0.05 and P() = 0.05


To Find: i) The probability that neither of them is available when needed


Here, P(not A and not B) = P()


= P() P()


=0.05 0.05


= 0.0025 =


Therefore, The probability that neither of them is available when needed is


ii)an engine is available when needed


Here, P(A and not B or B and not A) = P( A ) + P(B )


= P(A) P() + P(B) P()


= (0.95 0.05 + (0.95 0.05 )


= 0.0475 + 0.0475


= 0.095


=


Therefore, The probability that an engine is available when needed is


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