20 Mar 21
@joe-shmo saidThanks Joe.I understand all that but I don't think google sheets has a probability function as such
if you have a spreadsheet handy; using the general formula BigDoggProblem derived you can verify the following sum for the ways to read/not read set X :
P( n = 0) + P( n = 1) + P( n = 2) + ... + P( n = 99) + P( n = 100) = 1
[101 terms in total ]
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20 Mar 21
@venda saidIf you understand, that works for me!
Thanks Joe.I understand all that but I don't think google sheets has a probability function as such
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20 Mar 21
1 edit
@bigdoggproblem saidCorrect!
Probability for n>=4 is ~= 48.1%
The probability of at least 4 people reading set X in class of 100 is nearly 50%
P( n ≥ 4 ) = 1 - [ P ( n = 0 ) + P( n= 1 ) + P( n = 2 ) + P( n = 3 ) ] ≈ 48.1%
20 Mar 21
@joe-shmo saidI found it a bit strange that the probability for n=3 is the highest of all n's.
Correct!
The probability of at least 4 people reading set X in class of 100 is nearly 50%
P( n ≥ 4 ) = 1 - [ P ( n = 0 ) + P( n= 1 ) + P( n = 2 ) + P( n = 3 ) ] ≈ 48.1%
n prob
0 2.63%
1 9.75%
2 17.88%
3 21.64%
4 19.43%
5 13.82%
6 8.10%
7 4.03%
8 1.74%
9 0.66%
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21 Mar 21
@bigdoggproblem saidI can’t think of any logical reason at the moment why that should be. It’s not odd that there is a max. The binomial distribution is symmetrical, so that factor would skew it toward the middle (50). But the remaining factor heavily skews it toward the beginning. So i would kind of expect a maximum for sure between 0 and 50. The fact that it’s so heavily skewed is interesting.
I found it a bit strange that the probability for n=3 is the highest of all n's.
n prob
0 2.63%
1 9.75%
2 17.88%
3 21.64%
4 19.43%
5 13.82%
6 8.10%
7 4.03%
8 1.74%
9 0.66%