To find the expected value of the profit for the insurance company, we can use the following formula for the expected value $E(X)$:

$E(X) = x_1 \cdot P(x_1) + x_2 \cdot P(x_2)$

From the provided information:

• The profit $X$ can be either $-44100$ (if the woman dies, the company pays out the benefit) or $2900$ (if she survives, the company keeps the premium).
• The probabilities associated with these outcomes are $P(-44100) = 0.0602$ and $P(2900) = 0.9398$.

Let's substitute these values into the formula:

$E(X) = (-44100 \times 0.0602) + (2900 \times 0.9398)$

Calculating each term:

1. $-44100 \times 0.0602 = -2652.42$
2. $2900 \times 0.9398 = 2725.42$

Now, summing these results:

$E(X) = -2652.42 + 2725.42 = 73$

Thus, the expected value of the profit is $73.

Would you like further details on this calculation or have any questions?

Here are five related questions to expand your understanding:

1. What factors influence the probability values in life insurance policies?
2. How would the expected value change if the probability of survival increased?
3. What impact would a higher premium have on the expected profit?
4. How would the calculation change if there were additional outcomes (e.g., partial payouts)?
5. What is the significance of expected value for insurance companies?

Tip: Expected value helps companies understand the average outcome over many similar policies, guiding pricing strategies to ensure profitability.