There are 3 empty boxes (A,B,C) where each box filled with 100 numbered balls (number 00 to number 99) each box. Every play cost me 1 coin and allow to select 1 number from 00 to 99, then a ball is drawn from each box.
There are prizes to be won as below:
Pool Prize : All 3 boxes draws same with your selection, Initial Pool is 100 coins and it will increase by 1 coin if the pool not hit.
Prize A : Box A draws the same number to your selection, 30 coins.
Prize B : Box B draws the same number to your selection, 20 coins.
Prize C : Box C draws the same number to your selection, 10 coins.
My question:
How do I calculate my chances on hitting the pool and proof that my expected value will become favor to me (from lost to earn)?
To proof my losses of coins control at -8% (negative 8 percent) when I hit the pool? Example: I hit the pool on the 1,000th play, 1,000 coins on play but sum on my return is 920 coins, i lost 80 coins (8% of coins from 1,000 coins)
Logical assumption and changes allowed for no.2.
What I understand:
Each number has a probability of 1% where 1/100 = 0.01 (1%)
Hitting Box 1, 2, 3 = 30, 20, 10 Coins (each has 1% chance)
Return rate = 0.3, 0.2, 0.1 on every of my play and lost 0.4 each play.
Total Combination available is 100 x 100 x 100 = 1,000,000
1 chance out of 1 million combination hitting the pool, where 0.01 x 0.01 x 0.01 = 0.000001 (0.0001%)