Binary probability

Doos

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Jan 29, 2014
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Hi ,

I hope somebody can help in relation to the question below.

If we have a stream of data consisting of binary 1s and 0s and the 1 occurs with three times the probability of the 0, calculate the information in a 1 and a 0.

I would have thought something along the lines of 2^3 = 8 (1's) how many 0's ???

Regards.
 
If we have a stream of data consisting of binary 1s and 0s and the 1 occurs with three times the probability of the 0, calculate the information in a 1 and a 0.
Because of where you posted this, I will assume you are asking a simple probability question.
That is, I assume that this is not an information theory question.

Lets say that \(\displaystyle \mathcal{P}(0)=p\) then \(\displaystyle \mathcal{P}(1)=3p\).

Because \(\displaystyle p+3p=1\) then \(\displaystyle p=0.25\).

Now the probability that a binary-string of length \(\displaystyle N\) contains \(\displaystyle K\) 1's and \(\displaystyle N-K\) 0's is:

\(\displaystyle \dbinom{N}{K}(0.75)^K(0.25)^{N-k}\).
 
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