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:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15