Answer:
a) Monetary values corresponding to the two events are:
-In case of surviving the year = -166$
-In case of a death in the year = 89834$
b) Expected value of the purchasing the insurance is -85 $
c) Yes, insurance company can make a profit with this policy.
Step-by-step explanation:
<em>a)</em> The man need to pay 166$ first to enroll the insurance policy. If he survives within a year, he will lose 166$. Otherwise, if he dies within a year he will profit 89834$.
<em>b)</em> Expected value of the purchasing the insurance as following:
<u>-In case of surviving the year:
</u>
Value: -166$
Probability: 0,9991
<u>-In case of death in a year
</u>
Value: 89834$
Probability: 0,0009
Expected value is E(x) = -166×0,9991 + 89834×0,0009 = -85 $
<em>c)</em> Lets consider that 10000 different 31 year old man enrolled to this insurance policy. According to probability of death, 9 out of 10000 man expected to be dead within the year. Therefore, company need to pay 9*90000 = 810000$ to their costumers. But, company will collect 10000*166=1660000$ from their costumers in the beginning of the year
So, it is expected that company is going to profit 1660000-810000=850000$ per year.
![\left[\begin{array}{ccc}\boxed{\boxed{ 4/6 = 6/9}}\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cboxed%7B%5Cboxed%7B%204%2F6%20%3D%206%2F9%7D%7D%5Cend%7Barray%7D%5Cright%5D%20)
This would be because 4/6 is almost 1 as a whole, and also, 6/9 is almost 1, as a whole, so this would totally make sense for this to be a proportional.