In Lookout, CA there are three car owners, one car thief, and an insurance compa

Question

In Lookout, CA there are three car owners, one car thief, and an insurance company. Every year, one, and only one, car gets stolen with equal chance. The insurer offers a $14,000 policy at a $6,000 premium.

(1) What are the chances of turning negative profits if the insurer services only two car owners? (Round to the hundredths place.)

(2) What is the expected profit?

(1) What are the chances of turning negative profits if the insurer services all three car owners?

(2) What is the expected profit now?

Explanation / Answer

here probability =1/3 for all (as equal chances of stealing from 3 cars)

1)chances of turning negative profits if the insurer services only two car owners is

let p be chances of negative profit, as insurance company servicing 2 owners , it receives premium =2*6000

=$12,000. So

(p*14000)-12000 = 0

=> p =12000/14000

=0.857

=0.86 (appx)

2) expected profit = 6000*3 - (1/3*2*14000)

=$8,666.67

1)chances of turning negative profits if the insurer services all three car owners =

=> as premium receiving =6000*3 =$18000 which is more than $14000 policy, hence 0% chances of negative profit.

2)expecteds profit =6000*3 -14000

=$4000

=>expected profit =$4000

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