Question

Fire Fighters A house in Pana, Illinois was found to be so infested with cockroaches, that city council ordered fire fighters to burn it down rather than call in professional exterminators to deal with the problem. The town has three fire engines operating independently. The probability that a specific fire engine is available when needed is 0.96.

(a) What is the probability that none are available when needed?

(b) What is the probability that all three fire engine are available when needed?

(c) What is the probability that at least one engine is available?

(d) What is the probability that at least one engine is available?

Answer 1

X ~ Bin(n,p)

Where n = 3 , p = 0.96

Binomial probability distribution is

P(X) = ⁿC_x p^x ( 1 - p)^n-x

a)

P(X = 0) = ³C₀ * 0.96⁰ (1 - 0.96)³  

= 0.0001

b)

P( X= 3) = ³C₃ * 0.96³ (1 - 0.96)⁰  

= 0.8847

c)

P(X >=1) = 1 - P( X = 0)

= 1 - ³C₀ * 0.96⁰ (1 - 0.96)³  

= 1 - 0.0001

= 0.9999

d)

P(X >=1) = 1 - P( X = 0)

= 1 - ³C₀ * 0.96⁰ (1 - 0.96)³  

= 1 - 0.0001

= 0.9999

[ Option C and d are same questions ]