Question

A charity is holding a raffle to raise money. There is one car worth $30,000 and five $100 gift cards being raffled off. Each ticket costs $20, and there are a total of 5,000 tickets being sold. Which equation correctly depicts the calculation of the expected value for a ticket?

Answer 1

Answer: The required equation is,

$29980(\frac{1}{5000})+80(\frac{5}{5000})-20(\frac{4994}{5000})$

Step-by-step explanation:

Since, the total number of tickets = 5000,

In which Each ticket costs $20,

Also, There is one car worth $30,000 and five $100 gift cards being raffled off,

Thus, by these informations we can make the following table,

Number of tickets          1                5                4994      

Listed price($)           30,000          100               0

Loss                             20               20                20

Actual price($)           29980           80                -20

Probability                 1/ 5000       5/5000         4994/5000

We know that,

Expected value = Actual value × Probability,

Hence, the expected value for a ticket

$=29980(\frac{1}{5000}) + 80(\frac{5}{5000})-20(\frac{4994}{5000})$

Which is the required equation.

Answer 2

There is a total of $35,000 worth of prizes being given out for 5,000 tickets.  We can find the expected value for each ticket by dividing 35,000/5,000.  This equals $7.00.