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Probability of survival is a key concept in insurance, particularly when providing risk assessments for policies like life insurance. In this context, it's the likelihood that the insured individual will continue living over a specified period, such as a year. Calculating this probability allows insurance companies to estimate the risks and set appropriate premiums. In the exercise provided, the woman has a survival probability of 0.999057 for the coming year. This means that out of 1,000,000 similar individuals, approximately 999,057 would be expected to survive the year.
It's a small window for error but crucial for calculating other insurance metrics. Understanding this helps insurance companies balance the potential payout risks with expected incomes from premiums.

A life insurance policy is a contract between the policyholder and an insurer, where the insurer agrees to pay a specified amount (the policy's "face value") upon the policyholder's death. In exchange, the policyholder pays a regular premium to the insurer. In this exercise, the policy is worth $100,000, with an annual premium of $360. It is a term life insurance policy, which means it covers a specific period, such as one year. The main factors determining a policy's premiums include the age, health, and lifestyle of the policyholder. The probability of survival directly impacts these premiums since a higher likelihood of survival reduces potential payouts. Life insurance provides financial security for the policyholder's beneficiaries and often necessitates a thorough risk assessment by the insurance company.

Expected value is a statistical measure that can indicate the average outcome of a probabilistic event. For insurance companies, the expected value calculation helps determine the profitability or expected loss of issuing a policy. It combines the monetary outcomes and their probabilities to yield a single, comprehensive figure.For the woman's life insurance policy, we compute the expected value by considering both possible outcomes: if she survives or if she does not.

• If she survives, the company benefits from the \(360 premium.
• If she does not, the company pays \)100,000 but still keeps the $360 paid upfront.

Thus, expected values are calculated: \[E_{\text{survive}} = 360 \times 0.999057\]\[E_{\text{not survive}} = (-100,000 + 360) \times 0.000943\]The total expected value is the sum of these outcomes:\[E = (360 \times 0.999057) + ((-100,000 + 360) \times 0.000943)\]The results indicate the insurance company's expected profit or loss for this policy, informing decisions on pricing and risk management.