Question

A life insurance company sells a $240,000 one year term life insurance policy to a 25-year old female for $225. The probability that the female survives the year is .999572. Find the expected value for the insurance company.

Answer 1

$773.3587

Explanation:

The probability that the female survives = 0.999572

therefore, probability that female dies = 1-0.999572 = 0.000428

if the female survives the insurance company makes = $225

x=$250

If the female dies the insurance company pays $240,000.

So, the amount with the company = 240000-225 = $ 2390775

Therefore Expected value = 250(0.999572)-2390775(0.000428)= $773.3587

Answer 2

$122.28

Explanation:

Give the following :

Insurance worth = $240,000

Price sold = $225

P(survival) = 0.999572

P(death) = 1 - 0.999572 = 0.000428

If she survives, insurance firm makes $225

If she dies, insurance firm pays $240,000, hence the company losses :

$(225 - 240,000) = $−239775

Expected value (E(x)) = sum of P(i) * X(i)

E(x) = (P(survival) * profit made) + (P(death) * loss incurred)

E(x) = (225 * 0.999572) + (0.000428 * −239775)

= 224.9037 - 102.6237

=$ 122.28