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