1. suppose A B C = does it follow that p (A U B U C) = P(A) + P(B) + p(C)? Show that your answer is correct: give a proof if it does follow a counter example if it doesn't

2. prove that if p(A/B) = P(A/B) the A is independent of B

3 email filter look for common phrases used in spam. suppose 60% of emails is spam and 10% of spam emails use the phrase "free money". only 1% of non -spam emails say "free money" what is the probability a random email will mention "free email"