Expert: Paul Klarreich - 2/3/2010

Question
Hi, would appreciate your input on the following matter:

If one was to consider the case of a 5 number draw from a pool of 42 numbers (1-42) - like in certain lotteries - is the probability of any 5 numbers being drawn equal to 5 consecutive numbers being drawn. Note that the order in which they're actually drawn is not a factor to consider - i.e. should the numbers 22,20,19,23,21 be drawn they're to be considered consecutive cos' they can be sorted that way - drawing sequence is not what I'm after here.

I understand that each number has an increasing probability of 1/42, 1/41, 1/40 ... and consecutive numbers would not be void of this probability - but wouldn't certain patterns (eg. consecutive numbers) have a weighting when considering probability.

Thanks.

Answer
Questioner: Jimmy
Country: Malta
Category: Advanced Math
Private: No
Subject: Probability of consecutive numbers in a number draw (like lottery).
Question: Hi, would appreciate your input on the following matter:

If one was to consider the case of a 5 number draw from a pool of 42 numbers (1-42) - like in certain lotteries - is the probability of any 5 numbers being drawn equal to 5 consecutive numbers being drawn. Note that the order in which they're actually drawn is not a factor to consider - i.e. should the numbers 22,20,19,23,21 be drawn they're to be considered consecutive cos' they can be sorted that way - drawing sequence is not what I'm after here.

I understand that each number has an increasing probability of 1/42, 1/41, 1/40 ... and consecutive numbers would not be void of this probability - but wouldn't certain patterns (eg. consecutive numbers) have a weighting when considering probability.

Thanks.
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If order is irrelevant, then any subset has the same probability as any other.

P({1,2,3,4,5}) = 1/C(42,5), since that is only one subset.

and so is:

P({5,7,19,27,38}) or any other random subset.