Independence explained

Here is a simple way to 'get' the meaning of independence in probability. First, recall the test for independence:

if P(A|B)=P(A) then A and B are independent. The probability of B doesn't affect the probability of A. Think of examples when this does and doesn't happen. Using examples can make these concepts easier to grasp.

Now, how do we get P(A|B) ? It is P(A|B) = P(AnB)/P(B) ...the little 'n' means the intersection. In words, p of a given b equals the intersection of a and b divided by the probability of b.

How do we get P(AnB)? By multiplying together P(A) * P(B). Think of a probability tree. So we can rewrite

P(A|B) as P(A) * P(B)/P(B). Now, probabilities are just numbers, so we can cancel out the P(B) on the right hand side, leaving just P(A). Do you get it now?