# Law of Total Probability/Bayes' Theorem

1. Feb 23, 2012

### XodoX

Can somebody explain to me, using an example, what those 2 theorems actually are? Like, when I see a problem, how do I know what I'm gonna use?

I know Total Probability is "unconditional Probability", but I don't really get that.

The other definition of conditional probability was P(E I F)= P(E$\bigcap$F)/P(F). Can't figure out what the difference is, when I use which one..etc.

2. Feb 23, 2012

### kai_sikorski

A lot of the time in probability problems it's easiest to break down the problem into mutually exclusive cases and deal with them separately. Like what's the probability that the sum of two dice is less than 6?

P(X1 + X2 ≤ 6) = P(X2≤5)P(X1=1) + P(X2≤4)P(X1=2) + P(X2≤3)P(X1=4) +P(X2≤2)P(X1=4) +P(X2≤1)P(X1=5)

So above in the sum you break down the cases based on the result of the first die.