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

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chafah zachary am 24 Mär. 2014
Kommentiert: Star Strider am 25 Mär. 2014
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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Star Strider am 25 Mär. 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 am 25 Mär. 2014
The request stated "How many code words have exactly three successive 0’s?" It doesn't say, "how many have just three zeros and these must be successive." I see precisely twelve different six-bit words that have exactly three successive zeros, regardless of whether there might be other zeros:
000100
000101
000110
000111
001000
010001
011000
100010
100011
101000
111000
110001
However Chafah is the final arbiter of what was meant in the request.
Star Strider am 25 Mär. 2014
OK. I read it differently at the outset.

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Roger Stafford am 24 Mär. 2014
That's the kind of problem that can be solved mentally faster than a program can be written to do it. So why bother using matlab?
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