# Thread: expected value - probability demystified

1. ## expected value - probability demystified

hello guys
i have been reading a book called probability demystified written by
a. g. bluman, the answer he gives to the following question has me
mystified!!!! here is the question and his answer

One thousand tickets are sold for $2 each and there are four prizes. They are$500, $250,$100, and $50. Find the expected value if a person purchases 2 tickets his answer = -$0.20 cents

i think it a mistake can any1 help?
tx

2. Originally Posted by jickjoker
hello guys
i have been reading a book called probability demystified written by
a. g. bluman, the answer he gives to the following question has me
mystified!!!! here is the question and his answer

One thousand tickets are sold for $2 each and there are four prizes. They are$500, $250,$100, and $50. Find the expected value if a person purchases 2 tickets his answer = -$0.20 cents

i think it a mistake can any1 help?
tx
You have a one in a thousand chance of winning the 500 prize.
So if someone gave you a ticket, your expected return, if there were only the one prize, would be 500/1000 = 0.50
Now, if there's a second prize, say 250, the chances of you winning that particular prize are 1/1000, so your expected value from that prize alone is 0.25, BUT there's also the chance that you might win the 500, which has an expected value of 0.5, so between the two prizes, you'd expect to get 0.75.
Similarly for the 100 and 50 prizes.
Giving
500* (1/1000) + 250 * (1/1000) * 100* (1/1000) + 50* (1/1000)
= 0.9.
But you have two tickets, so you're twice as likely to win (approximately), so your expected return is 1.80.

But, if you paid 2 quid (total) for your two tickets, then your expected return is 1.80 - 2 = -0.20.

Perhaps the question in the book is phrased ambiguously?

3. you have answered the question with the tickets at 1 dollar each

the tickets cost 2 dollars each , so 2 tickets would cost you 4 dollars

with 1 ticket costing 2 dollars your expected value is -1.10 dollars

with 2 tickets costing 4 dollars ,he says you just double it - 2.20 dollars

so there must be a mistake in the book!!

5. Originally Posted by jickjoker