Randomly choosing one of two options with specified probability

I have two subroutines to be executed, one with probability p1 and another with probability p2 s.t. p1+p2=1, i am approching the problem in following methods:

say p1=0.6, p2=0.4, i need to perform the selection between 2 subroutine 10 times

1. Use function: out = randsrc(1,10,[1,2;0.6,0.4]); then choose routine 1 corresponding to 1 in output matrix and routine 2 corresponding to 2 in output matrix

here i'm getting output1: 2 1 2 2 1 2 1 2 1 1

executing again it is giving out: 1 1 2 2 2 2 1 2 1

expected output was number-1, 6-times and number-2, 4-times, but the output is not as expected.

2. use function: s = randsample([1,2],10,true,[0.6,0.4]);

3. use routine:

s=[];

for i=1:10

c = rand

if c<=0.6

select = 2;

else

select = 1;

end

s = [s,select];

end

method 2 and 3 are also giving the results as of method 1, can anyone help me to figure out the reason? or interpret the results as how they are following probability? or some other possible method to solve this problem.

[James Tursa]

Using rand, the output will be random (could select method 1 any number of times between 0 and 10). Did you want to always select method 1 six times, just in a random order?

[Shivani Agarwal]

I just want to ensure the correct probability of selection...that is my intution which i am not sure about, that if method 1 is selected six out of ten times randomly than correct probability of selection is followed. is there any other way to pick one of two subroutines with given probability?

[Ameer Hamza]

Shivani, the probability does not mean that the random numbers should be generated exactly in the proportion of probability density function. It just means that if you generate a very long series, the histogram of the generated numbers will approximately match the density function.

The "correct" depends on what you want to do. If your goal is just to follow the probability p1 and p2 in your question, then your code is already correct. But if your goal is to exactly run the two tasks in the proportion specified by p1 and p2 and the approach is given in my answer will be correct.

[Shivani Agarwal]

OK, I understood, Thanx for the explaination

Answer 1

[Ameer Hamza]

If you always want to keep fixed numbers of 1s and 2s, they try something like this

N = 10;
p2 = 0.4;

out = ones(1,10);
idx = randperm(10, floor(N*p2));
out(idx) = 2;

Result:

out =
     2     1     2     2     2     1     1     1     1     1
out =
     1     2     2     1     1     1     1     2     2     1
out =
     1     2     1     2     1     2     1     1     2     1