Life Insurance

Solution

Answer: $1,000,000

The probability that a 21-year-old dies during the year is \[ P(\text{death}) = 0.001. \] Thus the probability that they survive the year is \[ P(\text{survive}) = 1 - 0.001 = 0.999. \] If the person survives, the company's profit is \[ X = 150. \] If the person dies, the company collects the premium but must pay \(50{,}000\), so the profit is \[ X = 150 - 50{,}000 = -49{,}850. \] The expected profit is \[ E(X) = (150)(0.999) + (-49{,}850)(0.001). \] \[ E(X) = 100. \] If the company sells \(10{,}000\) policies, the expected total profit is \[ 10{,}000 \times 100. \] \[ = $1{,}000{,}000. \]