# how can I use matlab to solve this probability problem?

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Consider a binary code with 6 bits (0 or 1) in each code word.

(a) How many code words have exactly three successive 0’s? (b) What is the probability of the code word 000111?

I tried using matlab to no avail.

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### Accepted Answer

Star Strider
on 25 Mar 2014

I guess I’m revealing my intellectual ineptitude for all to see, but I actually wrote a short routine to explore that.

First, the probability of 000111 is 1/64. That is obvious.

Allowing for repeated occurrences, so that 0000 would count as two occurrences for instance, this codelet surprised me with the result (length(z)):

for k1 = 1:64

q(k1,:) = dec2bin(k1-1,6);

z3{k1} = strfind(q(k1,:),'000');

end

z = find(cell2mat(z3));

I wouldn’t mind an analytical proof of this. It’s not obvious to me.

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Roger Stafford
on 24 Mar 2014

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