A large school in the UK offers its pupils the opportunity to learn several

non-English languages. It turns out that:
• 55% of pupils in this school choose to learn French;
• of the pupils who learn French, 40% also learn German.

(c) Additional information is now given that 33% of pupils in this school
learn German. Calculate the probability that a randomly chosen pupil
in this school who learns German also learns French.
(d) What percentage of pupils in this school study either French or
German, or both?
(e) For pupils in this school, are the events of studying French and
studying German independent? Give a reason for your answer.
Please help