10   4. A large college produces three magazines. One magazine is about green issues, one is about equality and one is about sports. A student at the college is selected at random and the events G, E and S are defined as follows G is the event that the student reads the magazine about green issues E is the event that the student reads the magazine about equality S is the event that the student reads the magazine about sports The Venn diagram, where p, q, r and t are probabilities, gives the probability for each subset. G E S r q p t 0.08 0.09 0.05 0.36 (a) Find the proportion of students in the college who read exactly one of these magazines. (1) No students read all three magazines and P(G) = 0.25 (b) Find (i) the value of p (ii) the value of q (3) Given that P(S | E) = 5 12 (c) find (i) the value of r (ii) the value of t (4) (d) Determine whether or not the events (S ∩ Eʹ) and G are independent. Show your working clearly. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________