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?
Algebra ->
Probability-and-statistics
-> 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?
Log On
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?
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.
----------------------------------------
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.
(