Statistical Problem
https://www.theanswerbank.co.uk/Science/Question1804544.html
Question posted by Rev. Green on 10:15 Mon 25th Jul 2022 in The AnswerBank.enThe AnswerBankFri, 24 May 2024 17:24:30 +0100Science1800so for example 100 equal (apart from colour) counters in a box, 99 blue, one white, how many go's on average to pick a white if blues always returned to the pot ? Is that what you mean
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305534
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305534Mon, 25 Jul 2022 09:24:53 +0100Yep, good precis, bobbinwales.
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305537
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305537Mon, 25 Jul 2022 09:30:31 +0100in my example I think its 100 go's on average.... so in your case it would be n?
Or is that oversimplistic
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305538
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305538Mon, 25 Jul 2022 09:30:43 +0100Sorry, bobbinwales, 2 is not the answer when there are 2.
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305543
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305543Mon, 25 Jul 2022 09:35:30 +0100why not-suppose its a white and a blue.... sometimes you'll get white in one go (half the time), sometimes not until second go goes (25% of the time?) , sometimes not until 3rd go(1/8thof the time?) , sometimes 4th time if your unlucky.... sometimes 10 or moreth times if your very unlucky.
Im assuming you stop once you find the white one
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305547
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305547Mon, 25 Jul 2022 09:41:25 +0100My mistake. It is 2.
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305548
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305548Mon, 25 Jul 2022 09:42:44 +0100there is 1/100 chance every time so it could gotten on go 1 or go 100 and any go in betwees so the average number of attempts will be 50. ie if you did it an infinite number of times the average would be 50.
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305550
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305550Mon, 25 Jul 2022 09:42:53 +0100so in general terms it's n/2
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305551
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305551Mon, 25 Jul 2022 09:43:34 +0100so 1/2 x1 plus 1/4 x2 plus 1/8 x 3 plus 1/16 x4 plus 1/32 x 5 ...??
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305552
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305552Mon, 25 Jul 2022 09:44:15 +0100Toratoratora... I may be out of my depth here or may of misunderstood but surely it could be sometimes 101 goes or 102 or...200 or..
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LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305555Mon, 25 Jul 2022 09:47:17 +0100Think I've solved it. Let the answer = S. There is a 1/n chance of finding it on the first go, and a 1-1/n chance of needing a second go, for which the chance is S+1, because you'll use and extra go. So S=1/n+(1-1/n)(S+1). Therefore S=n.
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305559
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305559Mon, 25 Jul 2022 10:06:13 +0100If there are N items and you are looking for precisely one of them, with replacement, then you want to work out the sum to infinity of
1/N + 2*(1/N)*(N-1)/N + 3*(1/N)*[(N-1)/N]^2 + 4*(1/N)*[(N-1)/N]^3 ...
etc. Write as (1/N)*Sum(i=1,infinity) i [(N-1)/N]^(i-1)
This is the same as
N* d/dN{Sum(i=1,infinity) [(N-1)/N]^(i)}
which is the same as
N* d/dN {((N-1)/N)/(1-((N-1)/N))
from geometric sum. This just simplifies to
N* d/dN{N-1} = N* 1 = N
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305560
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305560Mon, 25 Jul 2022 10:06:16 +0100I think my approach is better because you don't need to assume that the sum exists and is finite. If you did then for example you can "prove" that if
S = 1 -1 + 1 - 1...
then S = 1 - S, giving S = 1/2 , which is at best misleading
https://en.wikipedia.org/wiki/Summation_of_Grandi%27s_series
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305562
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305562Mon, 25 Jul 2022 10:15:19 +0100The average of 1 and 100 is 50.5, not 50 Toratoratora. That's (n+1)/2 as given in the question for the case when items are kept out after being selected.
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305579
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13305579Mon, 25 Jul 2022 10:31:57 +0100bob 10:47, yes ignore me, I dived in too quick.
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306135
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306135Mon, 25 Jul 2022 19:04:50 +0100another way of looking at this is too look at the average number of attempts figure for all possible items chosen.
If theres 1 item then its clearly 1.
if theres 2 items then 2 makes sense. If one is red and one is blue then it takes 2 go's on average to get a red (just as its 2 for a blue.). Could'nt be 1 for a red as it would have to be the same for blue too as there equally likely, but clearly one go can't give red AND blue, only red or a blue.
If 3 items (one red a blue &1 yellow) then 3 makes sense- 3 go's for a red, 3 for a blue, 3 for a yellow as there all equally likely .
Well makes sense to me in my mind but i realise I'm not explaining it well.
Maybe sciencenoob can explain it better but without all them complicated formulas which lost me?
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306596
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306596Tue, 26 Jul 2022 10:45:34 +0100https://en.wikipedia.org/wiki/Geometric_distribution
https://www.cuemath.com/geometric-distribution-formula/
Maybe thinking in terms of dice rolls helps, if you roll a fair dice six times then you expect to hit each number exactly once in the first six rolls.
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306629
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306629Tue, 26 Jul 2022 11:35:16 +0100Your Answer.. If the number of goes is n for some value of n, then it is n for the next higher value of n because, if there are n+1 items you'll select the correct item on the first go 1 in n+1 times, otherwise (i.e. n out of n+1 times) you'll have to find it among the remaining n items, which will take n further goes on average, i.e. n+1 goes on total, including the go you've already had. Repeating this argument shows it'll be n for all higher values of n. But the number of goes is n when n is 1, so it is n for all positive integers.
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306769
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306769Tue, 26 Jul 2022 15:44:54 +0100so much groping around that it reminds me of - - the house of commons
ter saah ! TTT will confirm this is a paraprosdokian....
There is a probability function - the expectation
the chance of drawing three barls if you try 25 times
and here the chance of drawing any blu barl if the chancce is .01 and you try one hundred times is - you are likely to draw ONE blue barl
If you have 1 in 100 blues, and you draw fifty times
the chance of drawing one is 1/2
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306788
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306788Tue, 26 Jul 2022 15:56:06 +0100on these figures
1/100 and 100 goes - you are very likely to get a POISSON distribution where the chances are really "no blue barl "and "one blue barl" - and there are no other relevant possibilities
This means if one has a chance of P(x) the other is 1-P(x)
yes I know I am courting screams of "who said blue barl what den?" from knowledgeable and articulate ABers
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306792
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306792Tue, 26 Jul 2022 16:01:48 +0100this comes up in another guise
very rare occurrences of side effects
If you estimate that a covid vaccine side effect is 1 in 10 000
how many do you have to follow up in order to be reasonably sure it is much less than that ?
3n - - 30 000
https://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306798
LALASciencehttps://www.theanswerbank.co.uk/Science/Question1804544.html?answer=13306798Tue, 26 Jul 2022 16:06:44 +0100