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Answers to questions 2 to 5 should be written as simple fractions or exact decimals. Answers to questions 6 to 8 using the normal distribution should be given to four decimal places. 1) Make a copy of this Venn diagram and shade (B n C) U A a {1] 2) Members of a sports club play either cricket {C}. football (F) or tennis (T). P [C] = 0.5, PM = 0.4, PIT] = 05 and P(C n T) = 0.2. No one plays both football and tennis: a} Draw a Venn diagram to illustrate these probabilities, showing the probability {4] in each region. b) Are the events C and T independent? You must justify your answer. {2] 3) A group of 50 students were asked about their courses. 10 of the 28 female students said they studied humanities, 10 studied arts and the rest studied sciences. 11 of the male students studied humanities. 9 studied arts and the rest studied sciences. 3} Draw a two-way table to illustrate this information. {2] One person is chosen at random. Find: b) P(Studies arts) {1) c} P(Studies humanitieleemale) {1] d) P(Ma|e|Studies sciences) {1] 4) Three events A, B and C are such that B and C are mutually exclusive and that A and C are independent. Given that, P(C) = 0.5, PM] = 0.6, PIE) = 0.3 and P (A n B) = 0.1. find: a) P (A n C) {1) b) PilAl {1) Cl P(C1A'l {1) d) PM 0 CllB'l {1)