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Lotteries: are consecutive numbers less likely?
By Terry Roche (M604) on Wednesday, July 19, 2000 - 12:57 pm:

Hello,

I found your web page by searching for "probability" - I am from Newcastle, Australia.

I'm interested in a particular problem - just because it has intrigued me for years.

I walk into a shop and take a lotto ticket - if I choose six numbers following each other (ie 1,2,3,4,5,6) do I have the same theoretical chance of them coming up as if I choose a random six numbers that are not sequential.

If each number has an equal chance of being selected (assuming that the painted number on the higher numbered balls does not make them heavier, etc) then there should be as much chance of the six sequential numbers coming up - or is there an additional calculation to incorporate the chance of numbers selected being sequential ?

Your mathematical assistance would be appreciated and would calm an otherwise vexing problem.

Regards

Terry Roche

By Sean Hartnoll (Sah40) on Wednesday, July 19, 2000 - 05:33 pm:

Terry,

Imagine the marking on the balls were not different numbers but different colours. It should be completely obvious that no particular sequence of colours will be favoured over any other. It is the same with numbers. Just because we have defined a special order 1,2,3,... etc. It isn't really special in any other sense than convention. So to answer your question: the sequence 1,2,3,4,5,6 is no less or more likely than any other sequence.

Obviously, that sequence, like any other, is unlikely to come up!

Sean

By Michael Doré (P904) on Thursday, July 20, 2000 - 12:11 pm:

While this is certainly true it doesn't mean to say that the chance of getting 6 consecutive numbers = chance of not getting 6 consecutive numbers. All it means is that the chance of getting a specific set of 6 consecutive numbers (e.g. 1-6) = chance of getting a specific set of non-consecutive numbers. However overall there are many more possibilities for the later, and if you add them all up you find:

The chance of getting 6 consecutive numbers is much less than the chance of not getting 6 consecutive numbers

Michael