Question

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $5 each and will sell 800 tickets. There is one $2,000 grand prize, three $300 second prizes, and fifteen $20 third prizes. You just bought a ticket. Find the expected value for your profit.

Answer 1

The expected value of the profit is $-1

Explanation:

The expected value of any discrete variable X is calculate as:

E(X)=X1*P(X1)+X2*P(X3)+...+X3*P(X3)

Where X1, X2, ..., X3 are the values that the variable can take and P(X1), P(X2), ..., P(X3) are their probabilities.

In this case the variable X is the dollars that can win, so:

X1=$2,000

X2=$300

x3=$20

X4=$0

Then the probabilities can be calculate as:

`P(X1)=(1)/(800)`

`P(X2)=(3)/(800)`

`P(X3)=(15)/(800)`

`P(X4)=(781)/(800)`

Replacing the variables and probabilities on the equation of expected value we get:

`E(X)=(2000*(1)/(800) )+(300*(3)/(800) )+(20*(15)/(800) )+(0*(781)/(800) )`

E(X)=$4

Additionally, the student bought a ticket by $5, so the expected profit can be calculate as:

Expected Profit = Expected Earnings - Cost = $4 - $5 = $-1

Finally, the expected value of the profit is $-1