Thread: How to describe the probabilty in this case?

If we receive a flow of bits of a particular length, how to describe it in function of the length L?
I am interested in the description of the probability of receiving the sequence "10".
p1: Probability of receiving 1
p0: Probability of receiving 0
px: Probability of receiving whatever

If L=3, we can have:
10x
x10
so, the probability is p=2*p1*p0*px

If L=4,
10xx
x10x
xx10
1010
Here, the probability is p=3*p1*p0*(px^2)+(p1*p0)^2

If L=5,
10xxx
x10xx
xx10x
xxx10
1010x
10x10
x1010
In this case, p=4*p1*p0*(px^3)+3*((p1*p0)^2)*px

...

How to describe the probability in general, using L as variable???

Originally Posted by jgonzalf

If L=4,
10xx
x10x
xx10
1010
Here, the probability is p=3*p1*p0*(px^2)+(p1*p0)^2

I don't think this is right because both 10xx and xx10 include 1010.

It is easy to calculate strings that don't contain 10. Such strings have the form 0...01...1 where each of the two parts can be empty.

You are right, emakarov, I will try to reformulate the problem. Thanks a lot.

Originally Posted by jgonzalf

You are right, emakarov, I will try to reformulate the problem.

Please explain exactly what you are looking for is a bit-string.