I have Keno game with modified rules and i need to calculate probability to win jackpot. (not the game itself).
Where is 75 numbers all together, five last numbers (71..75) are jackpot numbers.
For each game 10 to 15 random numbers are selected (from 1 to 75 without duplicates).
For the range from 1..70 ALWAYS exactly 10 numbers are selected.
If generated numbers are from 71 to 75 when overall count of selected numbers will be more than 10.
Once 10 numbers from 1 to 70 are selected game will stop.
selected numbers: 1,2,3,4,5,6,7,8,9,10
or : 71,1,2,3,4,5,6,7,8,9,10
or : 1,2,71,72,73,74,75,3,4,5,6,7,8,9,10 - in such case player wins jackpot.
Cost of each game is - 1$
Jackpot payout - 4000$
I need to know what is probability to win jackpot?
If probability is more than 1/4000 when game will go into negative payouts and it's a bad thing...
I don't know how to solve this correctly because it is not like 6/49 probability calculations since total count of selected numbers is not fixed.