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.,$P(M \cap S)$).  
Then I know 

$P(M \cap S)= P(M)+F(S)-P(M \cup S)$, (easily derived from a Venn Diagram)

but just wonder why I can't simply do $P(M\cap S)=P(M)\times P(S)$ 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.