So a co-worker was talking about someone’s stupid plan to always play the previous winning lotto numbers. I chimed in that I was pretty sure that didn’t actually hurt their odds. They thought I was crazy, pointing out that probably no lottery ever rolled the same five-six winning numbers twice in a row.
I seem to remember that I am correct, any sequence of numbers has the same odds. But I was totally unable to articulate how that could be. Can someone help me out? It does really seem like the person using this method would be at a serious disadvantage.
Edit: I get it, and I’m not gonna think about balls anymore today.
In: Mathematics
The odds of an event happening are 1 in (the number of different possible outcomes). To make it simple, use coins.
The odds of you flipping 3 heads in a row are 1 in 8, because the possible outcomes are:
H h h
H h t
H t h
H t t
T h h
T h t
T t h
T t t
And only one of those is H H H.
But if you have already flipped two heads, what are the odds that the next flip will be heads? 1 in 2. Because the possible outcomes are
H h t
And
H h h
And only one of those is h h h.
What came before doesn’t matter, because it’s a part of the outcome that can’t change anymore, so it is part of ALL future outcomes. So it has no effect on the odds of the next outcome.
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