AUSTRALIA LOTTO

Lotto! Pick your numbers! Buy a ticket! But, what (really) are the odds of you cashing in on that multi million dollar win of the Australian loto?


1- Identify the lottery rules.

In this example, you will choose 6 unique and different numbers from 1 to 42 (The Australian Loto). You win the jackpot if all 6 of your numbers match all 6 of their numbers - in any order.


2- Create the 6 needed factors:

X1 = 6/42 = 0.14 (Probability that one of the 6 picks will match your first number)
X2 = 5/41 = ~0.12 (Probability that one of the 5 remaining picks will match your second number)
X3 = 4/40 = 0.1... (Probability that one of the 4 remaining picks will match your third number)
X4 = 3/39 = ~0.07 (Probability that one of the 3 remaining picks will match your fourth number)
X5 = 2/38 = ~0.05 (Probability that one of the 2 remaining picks will match your fifth number)
X6 = 1/37 = 0.02... (Probability that the remaining 1 pick will match your sixth number)


3- Multiply all the factors together:

X1 * X2 * X3 * X4 * X5 * X6 = ~0.0000001906 (this is the probability you'll win)


4- Divide the answer into 1 to see the odds against you! You have a 1 in 5,245,786 chance of winning.

1 / 0.0000001906 = 5,245,786


You have a 1 in 5,245,786 chance of winning the Australian Loto.