00:01
So we're told about an insurance policy, and there are at most two claims per year.
00:06
We have an interesting formula for finding the probability.
00:10
The probability, the x is n, is a constant k, multiplied by the probability x is n minus 1.
00:20
And there are three possible values can be taken here.
00:24
No claims, one claim, or two.
00:27
We're told the probability of no claims is 0 .1.
00:33
So these are possible values of x and their probabilities.
00:39
So probabilities are n, really.
00:44
So what's 1 and what's 2? well, we're going to use this formula.
00:48
And from this, the probability of 1 claim is 0 .1 multiplied by this constant k.
00:54
So that's 0 .1k.
00:55
And two claims is k times 0 .1k, 0 .1k squared.
01:02
We want to find this probability here, 0 .1k squared.
01:06
How do we do that? well, we know another fact about this.
01:10
It's a probability distribution.
01:12
One of these three outcomes is going to happen, they're the only possibilities.
01:17
So they have to add up to 1.
01:20
So 0 .1k squared plus 0 .1k plus 0 .1 is a 0 .1 is a 0.
01:27
Equal to 1.
01:28
And now you should be seeing this and thinking, oh, i have a quadratic.
01:32
I should solve my quadratic.
01:34
And i'm going to do that.
01:36
I'm going to multiply all of this by 10, just to make my life a little bit easier...