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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!

jbom1 wrote:

42 draws I believe for 57 eggs.

I'm sure it's much quicker than that. I have the probability falling below 50% on the 10th egg.

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

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):

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.

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!

I apologise, Hakan - I misunderstood the number of eggs. The formula should then be

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?!

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!

Soup Dragon wrote:I'm still very impressed at the brains we have on this forum.

Thanks.