All Keynes, students have the opportunity to learn lore musical instruments. The instruments offered to the students that: are: guitar and saxophone. Among the students in the school, it turns out Fond ! ! 40% take guitar lessons; of those students who take guitar lessons, 25% also take saxophone lessons. (a) Let G denote the event 'take guitar lessons', and let S denote the event 'take saxophone lessons'. Write the information given in the two bullet points in symbolic form. (b) Calculate the probability that a randomly chosen student in this school takes lessons in both guitar and saxophone. (c) Additional information is now given that 50% of the students in this school take saxophone lessons. Calculate the probability that a randomly chosen student in this school who takes saxophone lessons also takes guitar lessons. (d) What percentage of students in this school take either guitar lessons or saxophone lessons (or both)? (e) For the students in this school, are the events of taking guitar lessons and taking saxophone lessons independent? Give a reason for your