A fire company keeps two rescue vehicles. Because of the demand on the vehicles and the chance of mechanical failure, the probability that a specific vehicle is available when needed is 90%. The availability of one vehicle is independent of the availability of the other. Find the probability that neither vehicle is available at a given time?

The probability that neither vehicle is available at a given time is 0.01

Step-by-step explanation:

Let us assume the two needed vehicles are A and Q.

Let P (A) be the probability of the vehicle A available when needed.

And, P (Q) be the probability of the vehicle Q available when needed.

Now, P (A) = 90 % = 0.90

⇒ P (not A) = 1 - P (A)

= 1 - 0.9 = 0.1

⇒ P (not A) = 0.1

Similarly, P (Q) = 90 % = 0.90

⇒ P (not Q) = 1 - P (Q)

= 1 - 0.9 = 0.1

⇒ P (not Q) = 0.1

So, the probability that both the vehicles are NOT available when needed

= P (not A) x P (not Q)

= 0.1 x 0.1 = 0.01

Hence, the probability that neither vehicle is available at a given time is 0.01