M'learned friend Mr Pokery points out that five consecutive numbers appeared in a recent daily lottery draw. "What are the chances of that, eh?" he asks.
The probability of a sequence of S balls appearing in a lottery where D draws are made from B balls is a moderately well-known result.
D! * (B-S)! * (B-S+1)
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B! * (D-S)!
It's the usual one-over-B-choose-D, modified for the constraints of the sequenced balls. I leave the details of the derivation as an exercise for the reader.
In this case, S = 5, D = 7, B = 27, and the probability is - roughly - 0.006. We'd expect this sort of thing to happen every 167 draws or so - about once every six months.
A sequence of 6 is somewhat less probable, and would return every 1922 games. That's once in 6.2 years, so we're not overdue.
In the main part of the main lottery, there will be a triple roughly once every 10 weeks; runs of four should happen once every three years.
And for UK Deal or No Deal
, a run of four consecutive boxes in the first five should happen once every 77 games; that they're all blue (or all red) is a once-in-180 game chance. A run of five is a once-in-five-years happening; taking out the bottom five (or the top five) is something that Noel will probably never see.
posted 10 Jun 2006, 09.10 +0100
Intellectual