There are 10 cars in the lottery, each at a cost of $100,000. There are also 1,000 consolation prizes, $1000 each. The total number of the tickets is 10,000,000. The price of a ticket is $2. Find the mathematical expectation of the lottery.

Explanation:

The mathematical expectation is the sum of the products of the of each outcome by its probability.

Calling E(X) the mathematical expectation, that is:

The possible outcomes and its probability are:

1) For the cars

2) For the consolation prizes

3) Mathematical expectation of the prizes

3) Cost

Now, you must subtract the price of a ticket, since it is a certain cost, this is, it has 100% probability.

4) Mathematical expectation of the lottery

It is the expectation of the prizes less the cost:

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)