Date: Mar 13, 2007 11:54 AM
Author: briggs@encompasserve.org
Subject: Re: Probabilities

In article <1173799560.186277.223040@8g2000cwh.googlegroups.com>, Anonymous writes:
> Hi all,
>
> I've got the following phrase:
>
> BABAAAAAABAAABBAAAAAABA
>
> I would like to calculate the conditional probability P(B|A).


To phrase it more clearly, you want the conditional probability
that the next symbol is a B given that the current symbol is an A.

(And perhaps you want to throw in that you want to choose the
current position uniformly in the range 1 through 23)

> If I use a logical thought, I get:
>
> P(B|A) = the_number_of_AB / the_number_of_A = 4 / 17 = 0.23


And you want to consider the A at the end of the string as being
"not followed by a B" even though this is arguably a degenerate case.

Yes, I'd consider this result to be correct, given that interpretation.

> and if I use the formula P(B|A) = P(B inter A)/P(A) I get:
> P(B inter A) = 4 / (23-1)
> and P(A) = 17/23 then:
>
> P(B|A) = 4/22 * 23/17 = 0.25


This time you did consider that the A at the end of the string to
be a degenerate case and threw it out. In effect, you are choosing
the "current position" uniformly in the range 1 through 22 now.

Yes, I'd consider this result to be correct, given that interpretation.

> So I would like to know why the "logical thought" is wrong and if the
> result is right with the formula.


Both results are correct. It just depends on whether you include or
exclude one particular boundary case.