 # Joint Probabilty

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”.

Exactly

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.