Question

what would the expected annual profit be for an insurance company if The company charges an annual premium of $110 for minor injuries. Actuarial Studies show that in case of an injury claim the company will Pay out an average of $900 for outpatient care in an average of $3000 for an overnight stay in the hospital they also determined on average each year there are five claims made that result in outpatient care for every 1000 policies and three claims made that result in an overnight stay out of every 1000 polities. What is the expected annual profit of an insurance policy for the company????

Answer 1

Data as per the information given:

Scenerio	x	P(x)	x* P(x)
no injuries	110	0.992	109.12
outpatient care	-790	0.005	-3.95
overnight stay	-2890	0.003	-8.67
Total	Total	1.000	96.50

In case of no injuries co gets = 110 ; Prob = 992/1000 = 0.992

In case on outpatient care claim, co gets = 110 - 900 = -790 ;  Prob = 5/1000 = 0.005

In case on overnight stay claim, co gets = 110 - 3000 = -2890   ;  Prob = 3/1000 = 0.003

Expectecd value = X * P(X)

Expectecd value = (0.992 * 110) + (0.005 * -790) + (0.003 * -2890) = 96.50

ANS: Expectecd value = 96.50