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## Statistics and probability

### Course: Statistics and probability>Unit 9

Lesson 8: More on expected value

# Term life insurance and death probability

Understanding an insurance company's sense of my chances of dying. Created by Sal Khan.

## Want to join the conversation?

• What If there is epidemic and many people die.
Wouldnt the company go bankrupt and most of people not receive their money?
• Good point. Insurance companies actually purchase their own insurance for events like that from even bigger insurance companies with even more money. For example, maybe Sal's insurance company can afford to pay out \$1 million per year so they are ok if only 1 person dies. If more than one person dies, then they can collect some of their insurance money (from the bigger company) so they can afford to pay the policies they sold. And if we new the premium the bigger company charged Sal's insurance company, we could calculate how likely the bigger insurance bigger thinks this is just like Sal did calculated above.
• How do you know the probability of death? I know they look into risk factors but how can a company be sure that they will make a profit from the investment?
• Generally things happen similar to how they have happened in the past. There is an incredible amount of statistics and data in regards to how and when people die. A company can take that data and build models that put the odds in their favor of making a profit.
• At why is it that at most 1 Sals out of 100 may die in order for the insurance company not to loose money? What's the explanation? Sal didn't give any here.
• Because each Sal only pays 1% of the insurance payout over the life of the policy. So in this case 100 Sals each pay \$10,000 for a total of \$1,000,000. For each Sal that dies, the insurance company needs to pay that Sal's family \$1,000,000. So if 2 Sals die the Insurance pay out \$2,000,000 but have only collected \$1,000,000 so they are losing money.
• If that one person in 100 died they would probably not die at exactly year 20. Given that they would die sometime earlier and stop paying premiums at that point, wouldn't the probability of death need to be <1% for the company to break even?
• I think the best way to look at this "contract" between the buyer and the insurer is that the insurer figures there is some probability p that the user will die during the 20 year interval. A reasonable assumption is that this probability is uniformly distributed over the 20 years, with the expected (mean value) of death being 10 years. At \$500/yr, this means the insurer can expect the buyer to have paid on average (in thousands of dollars) \$5K before dying. Suppose the buyer does die during the 20 year period. In this case the insurer will be out \$995K= \$1000K-\$5K. If the buyer does not die during the 20 years, then the insurer will have gained \$10K. Therefore the expected return for the insurer is -\$995Kp + 10K(1-p) with a probability of p that the buyer dies during the 20 years. The insurer wants this expected return to be >=0. Therefore the insurer is estimating that p satisfies -1005Kp + 10K >=0 or that p satisfies p <= 10/1005, which is slightly less than the 1/100 suggested in the video.
• I am having trouble finding a definition of Expected Value? Can somebody give me a definition and also if there is a general equation I can use for the problem sets?
• http://www.artofproblemsolving.com/Videos/index.php?type=counting#chapter11

I found these videos to be a great introduction to Expected Value. In fact, you should definitely give all the rest of their video library a try :)
• What are some of the things an insurance company would look at when estimating one's probability of death in the next say, 20 years?
• Typically the big 3 are Age, Gender, and Health (which includes things like BMI, family history, blood pressure, cholesterol, and most importantly "Are you a Smoker?"). Other things that get accounted for might include DMV records (do you have reckless driving tickets or DUIs), Occupational risks (are you a crab fisherman or skydiver?), and income level (This might not be considered directly, but in general if you purchase a bigger policy the insurance company assumes you will have better access to medical care and thus lower mortality) . Additionally, what country you live in plays a factor.

Source: work in life insurance
• Lets say a person who is in great shape gets a policy of 500/year and his family is guaranteed 1Million Dollars after his death. But he dies in a car accident a few days later. Then What?
• Death is death. If it was an accident, the policy pays off. That's the whole point of insurance. It deals with uncertainty.

(Most life insurance has an exclusion for suicide that takes place within some period of time after the policy is purchased, because if the person is planning suicide, then death is not uncertain).
• Why has Sal not accounted for the time value of money(interest rates) while calculating the net payment for 20 years? Does the insurance company considers the interest when they pay the insurance after 20 years(in case of death)?