ok, it is always less than, except when: 1) The two events are INDEPENDENT, and 2) At least one of them is either zero or 1. P(Me being French) = 1/number of countries in the world Not French.
So are you saying that the correct answer is D or B?
I would say we are all dead without cfaisok:)) And I will go with B:)
strangedays Wrote: ------------------------------------------------------- > Considering that: > > P(A and B)= P(A | B) x P (B) Joint probability = > Conditional probability x Probability (b) > > or > > P(A|B)= P (A and B)/ P(B) > > > There is a high probability than the result is B. Well…map here it is my early explanation
We all agree that answers A and C are out, correct? If events are independent, and each event has a probability of occurring = 1, than D doesn’t hold. If the events are not independent, and each event has a probability of occurring = 1, than D doesn’t hold. B holds in all cases because of “less than or equal to”.
It has nothing to do with independence. The only way they can be equal is if the probability of B is 1.
strangedays, yes the answer is B…you had no problem there but you did not explain when it P(AB) < P(A|B), and when they are equal. And yes, I stand corrected by wyantjs, they don’t have to be independent for the equal part to be true. However, either P(B) = 1 or P(A) = 0 will do. I think this is the right conclusion.
Wow, how much more off could I have been… these are the kinda silly mistakes that will cost me the exam… I was just trying to conclude that dividing by a number between 0 and 1 (not inclusive) will result in a larger result… and then portrayed it all wrongly sorry for the really wrong answer…
I knew what you meant, but I had to point it out as wrong!
Ok, if p(AB)/p(B) = P(A/B) and all these number are between 1 and 0, then of course P(A/B) has to be greater than p(AB)… For me the answer then is: Joint probability of A and B must always be: B) less than or equal to the conditional probability of A given B. And, independence has nothing to do with it… the only way the two will be equal is when the joint is null or when p(B) is one.