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:

17.08

correct me if i am wrong.

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.