# conditional probability

Something wrong with my logic? IF P(A|B) = P(AB)/P(B) and P(AB) = P(A)P(B) After plugging the second formula into the first aren’t we left with P(A|B) = P(A)? I know this is wrong, but why is it? I’ve been trying to figure this out for a while and It’s driving me a lil insane.

P(A!B) = P(AB)/P(B) Or P(A!B)P(B)= P(AB)

Let me illustrate my issue with an example from the book: Suppose that 5 percent of the stocks meeting your stock-selection criteria are in the telecommunications (telecom) industry. Also, dividend-paying telecom stocks are 1 percent of the total number of stocks meeting your selection criteria. what is the probability that a stock is dividend paying, given that it is a telecom stock that has met your stock selection criteria? my thoughts were P(dividend paying|telecom stock) = P(dividend paying and telecom stock)/P(telecom stock) = (.05*.01)/.05 =.01 This is wrong, and the answers in the back don’t really explain how they did it.

.01/.05 = 20%?

Grrr…I don’t know!

CP yeah that’s right. What is the thought process though? In my line of thought the .05s cancel each other.

bk yeah that’s right. What is the thought process though? In my line of thought the .05s cancel each other.

suppose u screened 100 stocks that meet ur criteria… 5 are telecom and 1 telecom pays divedend… so 0.2

i dont have the book with me right now, but P(AB) is not equal to P(A) x P(B) unconditionally

ah thanks well that makes sense and is a great way to think about it. But can someone tell me what’s wrong with this logic? my thoughts were P(dividend paying|telecom stock) = P(dividend paying and telecom stock)/P(telecom stock) = (.05*.01)/.05 =.01

If P(AB) = P(A)*P(B) then A and B are independent which you sort-of proved in a backward way by noting that this implies P(A|B) = P(A). Anyway, it is not generally true that P(AB) = P(A)*P(B) unless someone tells you that A and B are independent (or you know they are unrelated).

so is thinking it in terms like bk where I just stepped away from the situation/formulas and pictured 100 stocks the right way to do it? Or is there some formula that I should have used? What’s the long way of doing this (the scenic route)?

" P(dividend paying and telecom stock) = 1%" is the same as " Also, dividend-paying telecom stocks are 1 percent of the total number of stocks " so it’s not math or logic, just English.