Thread: Statistics - Expected win/loss for lottery question

Hello! I need help on this question. I've been thinking about it for ages and I have absolutely no idea where to start.

The local lottery sets up a game wherein a player has a chance of collecting $750. The player must choose a 3-digit number and if it matches, the player receives $750.
It costs $1 to play the game.
What is the expected profit (or loss) for each player?

I'm not sure if there was a thread on this before. I googled but the link was not valid anymore.

Please help! What theory/formula do I use here?

Thank you.

Hello,

Let X denote the earning for each game.
if the number doesn't match.
if the number matches.

The value you're looking for is , with x taking values from

Now let's calculate the probabilities.



Choosing a 3 digit number is equivalent to choosing randomly three times a number between 0 and 9 (except for the first digit).

YZT

-> probability to get the matching one :

-> probability to get the matching one :

-> probability to get the matching one :


Another way to do it, more direct, is to know that there are number between 100 and 999.


Hence, the probability of getting the right number is
The probability of getting a wrong number is


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Originally Posted by defygravityy

Hello! I need help on this question. I've been thinking about it for ages and I have absolutely no idea where to start.

The local lottery sets up a game wherein a player has a chance of collecting $750. The player must choose a 3-digit number and if it matches, the player receives $750.
It costs $1 to play the game.
What is the expected profit (or loss) for each player?

I'm not sure if there was a thread on this before. I googled but the link was not valid anymore.

Please help! What theory/formula do I use here?

Thank you.

Excluding 0 but including numbers like 001, 021 etc, there are 999 different three digit numbers. So your probability of winning $750 is 1/999 and of losing $1 (that is, winning $-1) is 998/999.

Expected profit ($) = (750)(1/999) + (-1)(998/999) = -248/999, which represents a loss.

If you're not allowed to include numbers like 001, 021 etc, then there are (9)(10)(10) = 900 different three digit numbers. The above logic stays the same .....