From the BBC:
Bulgarian lottery repeat probed
The Bulgarian authorities have ordered an investigation after the same six numbers were drawn in two consecutive rounds of the national lottery.
A mathematician said the chance of the same six numbers coming up twice in a row was one in four million. But he said coincidences did happen.
Not sure where the said mathematician got 4m-to-1 from. I did a bit of digging (googling, mainly), and found out that the Bulgarian lottery plays 42 numbers, and draws six.
Under the above conditions, the chance of a particular set of six numbers appearing is:
1/(42*41*40*39*38*37)/(6*5*4*3*2*1) = 1/5.2m
For two identical sets of numbers to come up twice, the chance of that happening is simply the chance of a particular set of numbers coming up.
I therefore argue that the chance of two identical sets of numbers coming up twice in a row is 1 in 5.2 million. Am I right or am I missing something here?
Sounds about as unlikely as you returning to The Filter^ regularly!!
Posted by: aje | September 18, 2009 at 11:27 AM
Given that the two sets of numbers have already turned up twice then the probability is 1
Posted by: Tim Worstall | September 19, 2009 at 10:56 AM
42!/(6!*36!) = 5,245,786
But to get that same combination twice in a row it would be 5.2m^2 right?
Posted by: aje | September 19, 2009 at 12:17 PM