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.,$P(M \cap S)$) given the information:

Total class size is 10; 7 students take Math and 5 students take Science. Only one student takes none of them. What is the probability that student take both Math and Science.

Then I know

$P(M \cap S)= P(M)+F(S)-P(M \cup S)=0.7+0.5-0.9=0.3$, (easily derived from a Venn Diagram)

but just wonder why I can't simply do $P(M\cap S)=P(M)\times P(S)=0.7\times 0.5=0.35$ in this case even if M and S seem to be independent events but the result is different). What's the intuition behind the product rule and why the answers are different?

Thanks.