Question

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96. 

(i) What is the probability that a fire engine is available when needed? 

(ii) What is the probability that neither is available when needed?

Answer 1

(i) P(atleast one engine is available) = (1 – probability of no engine available) 

= 1 – P(A’ ∩ B’) = 1 – P (A’) P(B’) 

= 1 – (0.04) (0.04) = 1 – 0.0016 = 0.9984 

(ii) P (A’ ∩ B’) = P (A’) P(B’) 

= 0.04 × 0.04 

= 0.0016