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A made-up company sells phone insurance for 600 rupees a year…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up company sells phone insurance for rupees a year. In a year, a phone is broken with probability , and then the company pays rupees for the repair. A phone is stolen with probability , and then the company pays rupees. Assume that a phone is not both broken and stolen in the same year. Find the expected payout per policy and the company's expected profit per policy. Then find the expected profit from policies.
Need a reminder? The key ideaShow
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The expected payout. rupees.
Step 2. Profit per policy. rupees.
Step 3. 2000 policies. rupees.
Answer: rupees, rupees and rupees.
Why people still buy it. For each customer the expected gain is rupees. But a customer pays a small, certain amount to avoid a rare, large loss. The company can carry the risk because, by the law of large numbers, its average payout over thousands of policies is steady.
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