An insurance company will sell a 90,000 one-year term life...

An insurance company will sell a $\$ 90,000$ one-year term life insurance policy to an individual in a particular risk group for a premium of $\$ 478$. Find the expected value to the company of a single policy if a person in this risk group has a $99.62 \%$ chance of surviving one year.

An insurance company will sell a $\$ 90,000$ one-year term life insurance policy to an individual in a particular
risk group for a premium of $\$ 478$. Find the expected value to the company of a single policy if a person in this risk group has a $99.62 \%$ chance of surviving one year.

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Key Concepts

Probability

Probability is the measure of how likely an event is to occur. In insurance analysis, probabilities quantify the risks involved, such as the chance of a policyholder dying within a specified period, which in turn influences the premium setting and the insurer’s overall risk management strategy.

Risk Assessment in Insurance

Risk assessment in insurance involves evaluating the chance and impact of potential future events to determine the level of risk associated with an insured individual or group. By understanding and quantifying these risks, insurers can set premiums that are sufficient to cover potential losses while ensuring profitability over the long term.

Expected Value

The expected value is a key concept in probability theory and statistics that represents the average outcome of an uncertain event when repeated many times. In the context of insurance, it is used to calculate the average profit or loss by weighing each possible outcome (such as survival or death) by its corresponding probability, allowing companies to price policies effectively.

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