Except that we have 58 eggs to begin with (not 57) - the experimant was, after all, done before the actual draw.
But it's still only 9 eggs before the accumlated chances catch up!
re:the draw
- hwolge
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Re: re:the draw
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Re: re:the draw
Thanks John, you are correct - I only considered the probability of the first drawn station coming up again, neglecting the other stations that would be drawn. So, my series looked like (excluding the first draw):jbom1 wrote:I'm sure it's much quicker than that. I have the probability falling below 50% on the 10th egg.42 draws I believe for 57 eggs.
p(all unique after n draws) = (57/57)*(56/57)*(55/57)*(54/57) ..... *((58-n)/57)
p(1) = 1.000
p(2) = 0.982
P(3) = 0.948
p(4) = 0.898
p(5) = 0.835
p(6) = 0.762
p(7) = 0.682
p(8) = 0.598
p(9) = 0.514
p(10) = 0.433
P(first drawn station occurring again) = (1/57) + (1/57)*(56/57) + (1/57)*(56/57)^2 + ... (1/57)*(56/57)^(n-1)
At n = 40 the probability rises to 50.7%. If you include the first draw, this means that you would have to select 41 eggs (I think I said 42 above, which was a typo) before you had at least a 50% chance to encounter the station that was drawn first.
Sorry, the stations drawn in between didn't even occur to me. Yes, 10 draws is the correct answer.
Re: re:the draw
I apologise, Hakan - I misunderstood the number of eggs. The formula should then beExcept that we have 58 eggs to begin with (not 57) - the experimant was, after all, done before the actual draw.
But it's still only 9 eggs before the accumlated chances catch up!
p(all unique after n draws) = (58/58)*(57/58)*(56/58)*(55/58)*(54/58) ..... *((59-n)/58)
p(1) = 1.000
p(2) = 0.983
p(3) = 0.949
p(4) = 0.900
p(5) = 0.838
p(6) = 0.766
p(7) = 0.686
p(8) = 0.603
p(9) = 0.520
p(10) = 0.440
So I still have it going under 50% on the 10th egg (counting the initial selection as number 1) - someone may be able to put me right on the 1 egg discrepancy?!
- Soup Dragon
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Re: re:the draw
I love it when you maths boffins get all technical. I've never got a bloody clue what you're talking about but I'm still very impressed at the brains we have on this forum. I'm sure we have the makings of a good quiz team amongst us!
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- tubeguru
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Re: re:the draw
Thanks.Soup Dragon wrote:I'm still very impressed at the brains we have on this forum.
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