Question

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $10 each and will sell 600 tickets. There is one $1,000 grand prize, two $400 second prizes, and ten $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 when the student council is hosting a drawing to raise money for scholarships

What is probaility?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event

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:

$P(X_1)=\dfrac{1}{600}\\\\\\P(X_2}=\dfrac{3}{600}\\\\\\P(X_3)=\dfrac{15}{600}\\\\\\P(X_4)=\dfrac{581}{600}$

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

$E(X)=(2000\times \dfrac{1}{600})+(300\times \dfrac{3}{600})+(20\times \dfrac{15}{600})+(0\times \dfrac{581}{600})$

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

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