00:01
In this problem, we are going to determine how much an insurance company can expect to make on a policy.
00:09
Now, in this problem, the insurance company charges $800 a year for car insurance.
00:15
And the company will pay $1 ,000 for a minor accident and $5 ,000 for a major accident.
00:21
Now, the probability of a motorist having a minor accident is 0 .2, while the probability for having a major accident is 0 .05.
00:29
And we need to determine how much the insurance company can expect to make on a policy.
00:35
Now, first of all, let us determine the expected value of how much the insurance company has to pay.
00:43
So if x represents a random variable, which represents the amount that the insurance company has to pay, then this will be equals to summation x times px, where x is the payoff and px is the probability of that respective payoff.
00:57
Now, first of all, the company will pay $1 ,000 for a minor accident.
01:02
So the first payoff is $1 ,000 and the probability that they will have to pay that $1 ,000 is equal to the probability of the motorist having a minor accident, which is given to be 0 .2.
01:14
So this will be 0 .2.
01:17
Next, because of the summation, we add the next payoff and the probability of that payoff...