# Math Help - small probability question

1. ## small probability question

It goes something like this:
There is a lottery that has a pot that is drawn at 1900 dollars.
Tickets can be bought for $5 each, and each ticket entered into the lottery will raise the pot by$5.
Three prizes will be given:
1st place: $1300 2nd place:$650
3rd place: \$300
You can enter as many times as you want, and you can also recruit an
unlimited number of friends to enter for you (within reason).
Each person can only win one prize.

I am trying to calculate the optimal number of tickets to enter to
gain the most profit from this, based on the odds. I want to calculate
two different points: one is where you have a 50% chance of winning a
prize, and the other is where you spend the same amount of money as
you expect to earn back (for example, if i expected to win back on
average (1300+650+300)/3= 750, I would want to calculate the
probability of me winning money if I spent 750 dollars on the lottery.

First I thought that 1 ticket is equivalent to a 3/380 probability of
winning (1900/5=380 total entries) but that doesn't seem right, so i
am stuck...

any light you could shed on the situation would be greatly appreciated

no i dont want my homework done for me, just any pointers on how to calculate the probability/ equations to use would be much appreciated