Answer: -5.5
WOKINGS
Given that the lottery has the following number of winners:
One $2000 winner
Three $500 winners
Ten $100 winners
Also Given,
A total of 1000 tickets are sold
Each ticket costs $10
The expected winning for a person purchasing one ticket is the sum of the products of the gain/loss and their corresponding probability.
There is one $2000 winner
There are 1000 tickets
The probability of winning $2000
= 1/1000
= .001
There are three $500 winners
There are 1000 tickets
The probability of winning $500
= 3/1000
= .003
There are ten $100 winners
There are 1000 tickets
The probability of winning $100
= 10/1000
= .01
Since each ticket costs $10
Everyone who buys a ticket automatically loses $10.
Therefore, the probability of losing $10 is 1
Now to calculate the expected winning for a person purchasing one ticket
= 2000(.001) + 500(.003) + 100(.01) – 10(1)
= 2 + 1.5 + 1 – 10
= -5.5
The expected winning is -5.5. This implies that a person playing this lottery can expect to lose $5.50 for every one ticket that they purchase.