Answered

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The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $7 each and will sell 500 tickets. There is one $1,000 grand prize, three $200 second prizes, and fifteen $10 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

Sagot :

Answer:

Given Below

Step-by-step 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:

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

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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