Question

An insurance policy sells for ​$1200. Based on past​ data, an average of 1 in 100 policyholders will file a ​$20,000 ​claim, an average of 1 in 200

policyholders will file a ​$50,000 ​claim, and an average of 1 in 500 policyholders will file an ​$80,000 claim. Find the expected value​ (to the​ company)

per policy sold. If the company sells 20,000 ​policies, what is the expected profit or​ loss?

The expected value is $_________? (simplify your answer)

The expected (loss or gain) is $____________?

Answer 1

a) Profit in case of no claim = $1200

Profit in case of $20000 claim = 1200 - 20000 = -18800

Profit in case of $50000 claim = 1200 - 50000 = -48800

Profit in case $80000 claim = 1200 - 80000 = -78800

P(no claim) = 1 - 1/100 - 1/200 - 1/500 = 983/1000 = 0.983

x	1200	-18800	-48800	-78800
P	0.983	0.01	0.005	0.002

Hence, the expected value is $590.

b) Total expected profit = 20000*590 = $11800000

Hence, the expected gain is $11800000.

Please comment if any doubt. Thank you.