Probability Question - Chances of Winning the Lottery
I understand that chances of winning the Lottery are incredibly slim and that, theoretically, every number has an equal chance of being picked by the machine. I understand that this is why people say the combination 1 2 3 4 5 6 is just as likely to come up as 34 27 15 1 9 24. However... I think I've managed to overthink this as now I am struggling to understand why a set of consecutive numbers is just as likely to come up as a set of non-consecutive numbers when there are a greater number of non-consecutive numbers that could be picked.
Could anyone possibly explain this to me?
Could anyone possibly explain this to me?
The point is that any *given* set of numbers is just as likely as any other - if I say "you're going to get 1,2,3,4,5,6", I'm just as likely to be right as if I say "you're going to get 1, 9, 15, 24, 27, 34". However, it's much more likely that I'm right if I say "the numbers that come up, *whatever they are*, will not be consecutive" - because, as you say, there's far more ways to get non-consecutive numbers. In the first case, I predicted the exact numbers; in the second case, I didn't.
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