Question

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $10 each and will sell 800 tickets. There is one $1,000 grand prize, four $300 second prizes, and fourteen $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent. $________.

Answer 1

Answer:

-$6.72

Explanation:

The cost of the ticket = $10

Let X be the possible profit on the ticket.

The probability distribution for X is given below.

Thus, the expected value for your profit is calculated below:

$\begin{gathered} E(X)=\sum xP(x) \\ =\left(1000\times\frac{1}{800}\right)+\left(300\times\frac{4}{800}\right)+\left(30\times\frac{14}{800}\right) \\ =3.28 \end{gathered}$

Subtract from 10:

$3.28-10=-\ 6.72$

The expected value for your profit is -$6.72.

Note: This means that if you play the game, you expect to make a loss of $6.72 (rounded to the nearest cent).