Question

An insurance policy on an electrical device pays a benefit of $2850 if the device fails during the first year. The amount of the benefit decreases by $950 each successive year until it reaches 0 . If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.29.

Find the expected benefit under this policy?

Answer 1

Let x : be the benefit amount

The probability of failure during that year is 0.29

The probability of success = 1 - 0.29 = 0.71

The probability that the device fails in the first year is

Benefit amount on the first year is $2850

The probability that the device fails in the second year is

Benefit amount on the second year is $2850-$950 = $1900

The probability that the device fails in the third year is

Benefit amount on the third year is $1900-$950 = $950

x	2850	1900	950
P(x)	0.29	0.2059	0.146189

The formula for Expected value is ,

          

          

The expected benefit under this policy is $1356.59

If you round this to nearest whole number, it would be $1357 .