How to create a probability tree and calc prob of each branch?

I have six events and each event has a known probability of occurring first. All six occur but the order is unknown. There is thus one starting point and 6! (thus 720) ending points. I need to know the sequence of events and probability associated with each end point. This is probability tree 101. How do I set up such a tree in MATLAB (I do have Stat Toolbox)?

Thank you.

Answer 1

[jeff bodington]

Perfect! Thank you. I did not know about "perms" and how to use reshape.

[Image Analyst]

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Answer 2

[Roger Stafford]

I assume that after the first event the following events occur with the same probabilities as the first events but conditioned on previous events not occurring. If so, do the following.

Let p be a vector of the probabilities of each of the events occurring first. These must sum to 1.

   n = length(p);
   r = perms(1:n); % Get list of all possible permutations
   q = prod(p)./prod(cumsum(reshape(p(fliplr(r)),[],n),2),2);

Then q will be a list of the probabilities of each of the corresponding permutations in r - that is, the probability of each "end point". The values in q will sum to 1 (except for round-off error.)

[jeff bodington]

Woops, the code for "q = ..." does not execute. I have trid to debug it but have failed so far. Can you please take another look. Thank you.

[Roger Stafford]

I suggest you break up the code for 'q' into the following steps and see at which step your trouble occurs. (I don't seem to have any trouble with it.)

   t1 = fliplr(r);
   t2 = p(t1);
   t3 = reshape(t2,[],n);      
   t4 = cumsum(t3,2);
   t5 = prod(t4,2);
   t6 = prod(p);
   t7 = t6./t5;

If n = 6, t1 should be a 720 x 6 array, t2 a 4320 x 1 vector, t3 a 720 x 6 array, t4 also 720 x 6, t5 a 720 x 1 vector, t6 a scalar (1 x 1), and t7 a 720 x 1 vector.