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Re: Probabilities
Posted:
Mar 13, 2007 11:54 AM


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(BA).
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(BA) = 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(BA) = P(B inter A)/P(A) I get: > P(B inter A) = 4 / (231) > and P(A) = 17/23 then: > > P(BA) = 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.



