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

Supose that F1, F2......Fn are events such that Fi[itex]\bigcap[/itex]Fj=∅ whenever i≠j and F1[itex]\bigcup[/itex]......[itex]\bigcup[/itex]Fn=S. Then for any event E,

P(E)= P(E I F1) P(F1)+....+P(E I Fn) P(Fn).

The other definition of conditional probability was P(E I F)= P(E[itex]\bigcap[/itex]F)/P(F). Can't figure out what the difference is, when I use which one..etc.Bayes' is for conditional probabilities, but apparently you calculate those conditional probabilities differently...

For any events E and F, the conditional probabilities P( E I F) and P(F I E) are connected by the following formula:

P(E I F)=P(F I E) P(E)/P(F)