00:01
So we have a population that 20 % of them have a chance of 2 % dying next year.
00:13
And 80 % of that population has a chance of 1 in 200, which is 0 .5 % death next year.
00:24
And they have a law of insurance that pays them a $100 ,000.
00:27
The question is, what is the fair premium for these two groups? so the fair premium is expected payoff.
00:34
That means likelihood of debt times the payoff.
00:37
Payoff is $100 ,000.
00:39
Likelihood of debt for group 1 is 2%.
00:43
For group 2 % for group 2 %.
00:45
So the premium of group 1 is 2%, which is likelihood of their debt times $100 ,000, which is $2 ,000.
00:54
And the premium for group 2 is likelihood of their debt, which is 0 .5 % times the payoff.
01:02
Which is $100 ,000, which gives them a premium of $500, right? so premium group of group one is $2 ,000.
01:12
Premium of group two is $500.
01:14
Now the question is if the company doesn't want to distinguish between these two groups and charges an overall premium to everybody, what would be that premium? and the premium would be, so you have 20 % of them which pay a premium of $2 ,000, and 80 % of them which pay a premium of 500.
01:37
So the average is going to be just multiplication 20 % times 2 ,000 plus 80 % time 500...