Lottery Probability Gains and Losses

Question

The LotLot Lottery has a game called pick 4 numbers from 1 to 9, where player pays 50 pesos. If the 4 numbers come up in any order, then the player wins 6,300 pesos. Then the expected amount of gains/losses by the player, in the long run, is ___ pesos.

Answer 1

In the lottery the four numbers can be selected in 9 C 4 ways

So probability of winning is ( 1 / 9 C 4) = 1 / 126

So if you play

You lose 50 pesos (gain -50 pesos) with probability 125 / 126

You win 6300 pesos with probability 1 / 126

So expected gain per play = (125/126) x (-50) + (1/126) x 6300 = 0.3968 pesos.

By Law of Large Numbers , this means if you play the game N times where N is large (>1000) you would expect over those games to make a profit of approximately 0.3968 N pesos.