A town has two fire engines operating independently. The probability that a specific engine is available when needed is 0.96. (a) What is the probability that neither is available when needed? (b) What is the probability that a fire engine is available when needed?

Answer is

a. P (both pumps not available) = 0.016

b. P (both pumps available) = 0.984

Step-by-step explanation:

a. Probability of neither pump is available.

We know that P1 + P2 = 1

P1 = Probability of one pump is available = 0.96

P2 = Probability of a pump not available = 1-0.96 = 0.04

Now the probability of both pump not available will be = P2 x P2

=0.04 x 0.04 = 0.016

b. Probability of both pumps available will be.

Using the equation of probability

P (both pumps available) + P (both pumps unavailable) = 1

P (both pumps available) = (1 - P (both pumps unavailable))

P (both pumps available) = 1-0.016

P (both pumps available) = 0.984