I'm looking for the formula to calculate the probability for the
Australian lotto. There is a pool of 45 balls, they draw 7 balls for
the jackpot and then 2 additional (bonus) balls which allow you to win
in the lower prize divisions. Thus in total 9 balls from the pool of
45. The prize divisions are:
7 balls
6 balls + 1 bonus
6 balls
5 balls + 1 bonus
5 balls
4 balls
3 balls + 1 bonus
I have calculated the odds of getting the 7 numbers for the jackpot as follows:
PERMUT(45;7)/PERMUT(38;0)/PERMUT(7;7) = 45,379,620
for 6 +1 as follows:
(FACT(7)/FACT(1))/FACT(6))*((FACT(38)/FACT(37)/FACT(1))*2/38)*45,379,620
= 3,241,401
for 6 numbers
(FACT(7)/FACT(1))/FACT(6))*((FACT(38)/FACT(37)/FACT(1))*36/38)*45,379,620 = 180,078
These all agree with the odds as advertised on their
site:http://www.lottery.wa.gov.au/asp/index.asp?pgid=561
I cannot fathom how to calculate the odds for the rest of the prize
divisions. The expected answers are:
5+1 = 29,602
5 = 3,430
4 = 154
3+1 = 87
For eg I used (FACT(7)/FACT(2))/FACT(5))*((FACT(38)/FACT(36)/FACT(2))*4/38)*45,379,620
= 29,202
to try and calculate the 5+1 division but as you can see it is out by
400. using the same formula for the rest of the divisions gives me the
following:
5 = 3,074
4 = 177
3+1 = 84
Anyone have any ideas? |
