Question

At a lottery ticket costs $2.  Out of a total of 10,000 tickets printed for this lottery, 1,000 tickets contain a prize of $5 each, 100 tickets have a prize of $10 each, 5 tickets have a prize of $1,000 each, and 1 ticket has a prize of $5,000.  If you buy one ticket, what is the expected value of your gain/loss? ← HW  

Answer 1

From the given data, the following Table is calculated:

Event	Value (x)	Probability (p)	x   p
1,000 tickets contain a prize of $5 each	5 - 2 = 3	1000/10000= 0.1	3 X 0.1 = 0.3
100 tickets have a prize of $10 each,	10 - 2 = 8	100/10000=0.01	8 X 0.01 = 0.08
5 tickets have a prize of $1,000	1000 - 2 = 998	5/10000 = 0.0005	998 X 0.0005 = 0.499
1 ticket has a prize of $5,000.	5000 - 2 = 4998	1/10000= 0.0001	1998 X 0.0001 = 0.1998
No prize	- 2	8894/10000=0.8894	- 2 X     0.8894 =    - 1.7788
Total =			- 1.00

So,

If we buy one ticket, the expected value = - $1.00 (Loss)