Question

A raffle has 10000 tickets. the grand prize wins a motorcycle worth $9000. additionally, there is one ticket that pays $2000 and another one that pays $1000. the remaining tickets will win nothing. if you have a ticket, what is the expected payoff for that ticket?
A)$.90
B)$1.00
C)$1.20
D)$1.80

Answer 1

To solve this problem we need to find arithmetic mean of the given prize values.
To find arithmetic mean of any series of numbers you simply add them all together and then divide them by the number of numbers in the series.
We can express this by following formula:
$A= \frac{1}{n}\sum_{i=1}^{n} a_{i}$
Where $a_{i}$ represents value of each number in the series.
In this problem, we have 10000 numbers. Most of them are zero because most tickets don't win anything.
We just add the value of all prizes and divide them by the number of tickets.
$A= \frac{9000+2000+1000}{10000} =1.20$
The answer is C. Your expected payoff is $1.2.