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| Expectations |
Expectations
The ‘expectation’ related to the outcome of an experiment is found by multiplying the probability of an event times its potential reward, or cost.
Insurance
Probabilities and expectations are fundamental concepts in the insurance industry.
For example, suppose the probability of a particular type of house burning down in any given year is one in a thousand, and the owner wants insurance against such a loss. How much should the insurance cost? For an insurance company to break even, the insurance fee should be equivalent to the expected loss, or one-thousandth of the value of the house. If the probability of a house burning down is lower, the fee should be lower. The system works because an insurance company has many customers, all paying fees matched to the value of their houses and the probability of that type of house burning down. Some years there may be lots of rain, few fires, and fewer insurance claims. During other years there may be an above average number of fires.
Insurance companies have to gather accurate data on the value of homes and the risk of house fires, and then use that data to calculate expectations. Similar factors apply to life insurance, and car insurance.
Estimating expectations
The ultimate contribution of probability to clear thinking occurs when you systematically make estimates of the expectations related to decisions that you are about to make.
For example, should you buy that lottery ticket? Suppose a lottery ticket costs $2, the grand prize is $20 million, and the probability of winning is one-in-14 million. Then the expectation for success is $1.43 (one-in-14 million x $20 million), while the expectation for failure is $2.00 (to the nearest cent). Over many lottery draws, you can expect to spend $2.00 in order to win $1.43. Perhaps there is $0.57 worth of entertainment in participating. At any rate, the lottery profits usually go to a good cause.
In summary, every decision involves choices, every choice has a probability of being successful, and every choice has consequences. With a basic knowledge of probability, you are more likely to pause and make an effort to analyze these factors in an objective manner.
The ‘expectation’ related to the outcome of an experiment is found by multiplying the probability of an event times its potential reward, or cost.
Insurance
Probabilities and expectations are fundamental concepts in the insurance industry.
For example, suppose the probability of a particular type of house burning down in any given year is one in a thousand, and the owner wants insurance against such a loss. How much should the insurance cost? For an insurance company to break even, the insurance fee should be equivalent to the expected loss, or one-thousandth of the value of the house. If the probability of a house burning down is lower, the fee should be lower. The system works because an insurance company has many customers, all paying fees matched to the value of their houses and the probability of that type of house burning down. Some years there may be lots of rain, few fires, and fewer insurance claims. During other years there may be an above average number of fires.
Insurance companies have to gather accurate data on the value of homes and the risk of house fires, and then use that data to calculate expectations. Similar factors apply to life insurance, and car insurance.
Estimating expectations
The ultimate contribution of probability to clear thinking occurs when you systematically make estimates of the expectations related to decisions that you are about to make.
For example, should you buy that lottery ticket? Suppose a lottery ticket costs $2, the grand prize is $20 million, and the probability of winning is one-in-14 million. Then the expectation for success is $1.43 (one-in-14 million x $20 million), while the expectation for failure is $2.00 (to the nearest cent). Over many lottery draws, you can expect to spend $2.00 in order to win $1.43. Perhaps there is $0.57 worth of entertainment in participating. At any rate, the lottery profits usually go to a good cause.
In summary, every decision involves choices, every choice has a probability of being successful, and every choice has consequences. With a basic knowledge of probability, you are more likely to pause and make an effort to analyze these factors in an objective manner.
