6/49 Lottery Question

Nigel · science forum beginner Joined: 03 Jun 2005 Posts: 37

How many draws of a 6/49 lottery before a particular triple (eg 1-2-3)
is more than 50% probable to have been drawn?

I took the approach that there are 18424 triples possible, of which 20
appear each draw. The probability of a particular triple not appearing
after 1 draw is therefore (18424-20)/18424. For subsequent draws, raise
to the power of the number of draws. Subtract the numbers from 1 to find
the probability of a particular triple have appeared by that draw. That
gives the answer that a particular triple is more than 50% probable to
have appeared by the 639th draw.

The reason that I'm not happy with this approach is that the 20 triples
per draw are not independent of each other. Intuitively I'd expect a
sort of mild clustering effect which would raise the number of draws of
the 50% watershed slightly.

Could someone help me with the correct answer please?

Thanks,

NigelH

Proginoskes · science forum Guru Joined: 29 Apr 2005 Posts: 2593

nigel wrote:

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