HELPFUL FORMULAS Additive Rule P( E F ) P( E) P( F ) P( E F ) Probability of the Complement P ( E ) 1 P( E ) Expected Value E m1 p1 m2 p2 ... mn pn Conditional Probability P( E F ) P( E F ) P( F ) Product Rule P ( E F ) P ( F ) P( E F ) Product Rule for Independent Events P( E F ) P( E) P( F ) Bayes' Theorem P[ Aj E ] P[ E Aj ] P[ Aj ] P[ E A1 ] P[ A1 ] P[ E A2 ] P[ A2 ] P[ E An ] P[ An ]