# How to pick a value according to its probability

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Steven on 7 Dec 2011
Commented: Real User on 28 Apr 2023
Hi,
Let's say
P = [0.1 0.3 0.4 0.2]
X = [1 2 5 9]
where P(n) is the probability to select the X(n) element. I wish to make a function that select a "random" element of X according to its probability, like
f = myfun(P,X)
>> f = 2 (occurs around 30%)
thx a lot
##### 4 CommentsShow 2 older commentsHide 2 older comments
Walter Roberson on 3 Nov 2016
AB = [a,b];
AB( randi([1 2]) )
PANTHAGADA ANIL KUMAR on 16 Apr 2020
how to select an element with least probablility

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### Accepted Answer

Sean de Wolski on 7 Dec 2011
f = X(find(rand<cumsum(P),1,'first'))
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Walter Roberson on 7 Dec 2011
The answers in the other thread took care in case cumsum(P) < 1 as can happen due to round-off error.

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### More Answers (3)

Jonathan on 3 Sep 2018
Edited: Jonathan on 3 Sep 2018
The accepted answer is not doing any sanity check, and is sensitive to rounding errors. You should use randsample instead.
To sample n points from X, with replacement, and probabilities P:
randsample( X, n, true, P )
This can also be used with a custom RandStream (see documentation). Be aware that this function does NOT check for negative values in P; check manually if needed.
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krishna teja on 20 Apr 2020
searched a lot for this kind of function
Real User on 28 Apr 2023
randsample() seems to require Statistics and Machine Learning Toolbox

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Steven Lord on 16 Apr 2020
You can use discretize (which didn't exist when this question was asked originally) to do this. Generate uniform random numbers, bin them using bins whose widths are given by P, and for each bin return the corresponding element of X.
P = [0.1 0.3 0.4 0.2];
X = [1 2 5 9];
values = discretize(rand(1, 1e4), cumsum([0 P]), X);
histogram(values, 'Normalization', 'probability')
The probabilities shown in the histogram should agree pretty closely with the values in P.
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Mendi on 9 Jul 2021
The fastest one (100ns-200ns):
function [idx] = get_random_choice(p)
% Random choice with probability
% Example: get_random_choice([0.2,0.7,0.1])
N=length(p); idx=1; cump=0;
r=rand;
while(idx<N)
cump=cump+p(idx);
if(cump>r),break,else,idx=idx+1;end
end
end
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