# Math Help - Probability Question

1. ## Probability Question

I have some homework that I cannot figure out because of this formula:

$P(B|A) = \frac{P(A and B)}{P(A)}$

I don't exactly understand the above formula for calculating the probability of B given A. (So basically I don't understand what the probability of "B given A" means and when to use it.) If someone could explain this to me, it would be greatly appreciated.

2. Hello,
Originally Posted by Cursed
I have some homework that I cannot figure out because of this formula:

$P(B|A) = \frac{P(A and B)}{P(A)}$

I don't exactly understand the above formula for calculating the probability of B given A. (So basically I don't understand what the probability of "B given A" means and when to use it.) If someone could explain this to me, it would be greatly appreciated.
The probability "B given A" is the probability for B to happen if A already happened before. So we know A happened before and we're studying the probability for B to happen under this condition.

If you multiply it by the probability of A to happen, you'll have the probability :
- that A happens
- that B happens, since you suppose B happens if A happens

So that's why basically P(A and B) is P(B|A)P(A).
Maybe it helps to see it this way, dunno...

Imagine you have a soccer match. Teams A and B have the same probability to score (0.5). A player from team A scores (event A). This will make the players of team A very happy and they will be less careful. On the other hand, players from team B will do their best in order to score back, otherwise they'll be fired by their coach. So given the fact that team A scored first, the probability for team B to score (event B) will be superior, for example 70% !!
These 70% are the probability of "B given A".

And we have P(A)=0.5, P(B|A)=0.7

My explanations in English are just awful so if you have any questions...