Final answer:
The expected value of a single raffle ticket, when 3,300 are sold at $2 each with a $3,000 prize, is -$1.091. This number represents the average loss per ticket if the raffle is played repeatedly.
Step-by-step explanation:
The student wants to calculate the expected value of a single ticket in a raffle where 3,300 tickets are sold at $2 each, and one prize of $3,000 is awarded.
To find the expected value, we use the formula for expected value in a probability scenario, which is the sum of each outcome multiplied by its probability.
For this raffle, there are two possible outcomes for a ticket: you win the $3,000 prize, or you win nothing.
The probability of winning the prize is 1/3,300 since there is only one winning ticket. The probability of not winning is 3,299/3,300. We calculate the expected value (E) as follows:
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- Calculate the expected value if you win: (1/3,300) × $3,000 = $0.909.
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- Calculate the expected value if you do not win: (3,299/3,300) × $0 = $0. (Since there’s no monetary value associated with losing).
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- Add the two expected values together: $0.909 + $0 = $0.909.
Since a ticket costs $2, the net expected value is the expected win minus the cost of the ticket: $0.909 - $2 = -$1.091.
The expected value of holding a single ticket is therefore -$1.091, meaning that on average, a participant would lose $1.091 per ticket bought.