SOLUTION: In a raffle where 3500 tickets are sold for $2 each, one prize of $4800 will be awarded. What is the expected value of a single ticket in the raffle?

Question 1205333: In a raffle where 3500 tickets are sold for $2 each, one prize of $4800 will be awarded. What is the expected value of a single ticket in the raffle?

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Let's say one single person buys all 3500 tickets.

They would spend 3500*2 = 7000 dollars in total.
They would have 100% probability of getting the prize of $4800.
But they walk away with a net loss of 4800 - 7000 = -2200 dollars.

Divide this net loss over the number of tickets.
-2200/3500 = -0.62857 approximately
This rounds to -0.63 which is the approximate expected value.

The person should expect to lose, on average, around 63 cents per ticket.

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Another approach is to set up a table as shown below

Event	X	P(X)	X*P(X)
Win	4798	1/3500	4798/3500
Lose	-2	3499/3500	-6998/3500

where X = net earnings = amount you walk away with
Note that 4800 - 2 = 4798
P(X) = probability of getting those earnings

The X*P(X) column is the result of multiplying each X and P(X) value together.

Add up those X*P(X) values:
4798/3500 + (-6998/3500)
4798/3500 - 6998/3500
(4798 - 6998)/3500
-2200/3500
-0.62857 approximately
That leads to -0.63 when rounding to the nearest cent.

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Answer: -0.63 dollars

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