Deals 4 Wheels (D4W) leases a vehicle that can be operating in peak condition, a

Question

Deals 4 Wheels (D4W) leases a vehicle that can be operating in peak condition, average condition, or poor condition at the beginning of a customer's rental period. The vehicle is operating in peak condition at the beginning of 60% of the rental periods and will break down during the rental period with probability 0.01. The vehicle is operating in average condition at the beginning of 35% of the rental periods and will break down with probability 0.07. When the vehicle is operating in poor condition, it will break down with probability 0.30. What is the probability that the vehicle breaks down during a rental period?

Explanation / Answer

We have 3 states in which the leased vehicle operates in during the beginning of the customer's rental period: peak condition, average condition and poor condition.

The probability of being in the peak condition is 60% ie .6, probability of being in the average condition is 35% ie .35. Now the total probability is 1. So the probability of being in the poor condition is 1-.6-.35= .05.

Now probability of vehicle breaking down during peak condition is 0.01, probability of it breaking down during average condition is 0.07 while the probability of it breaking down during poor condition is 0.3.

So the total probability of the vehicle breaking down during a rental period= probability of being in a particular state*probability of breaking down during that state= .6*.01+.35*.07+.05*.3= 0.0455 ie 4.55%

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