In a certain class, 30% of the students failed in Mathematics, 20% failed in chemistry, 15% failed in Physics, 10% failed in both Math and Chemistry, 5% failed in both Math and Physics, 6% failed in Chemistry only and 3% failed in Math, Physics and Chemistry. If a student in this class is chosen at random, what is the probability that:
Hint: Use a Venn diagram to solve the problem.
1) he did not fail in Math nor in Physics nor in Chemistry? *
2) he failed in Math only? *
3) he failed in Physics only? *
4) he failed in Physics and Chemistry? *
5) he did not fail in Physics? *