I just bump into a simple question. let's say I want to compute the probability of taking both Math and Science course (i.e.,`P(M and S)`) 
Then I know `P(M and S)= P(M)+F(S)-P(M or S)`, but just wonder why I can't simply do `P(M)*P(S)` in this case even if M and S seem to be independent events (I tried but the results were different). What's the intuition behind the product rule and want to know why the answers are different?

Thanks.