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A box contains many pens that are of three colours; green, blue, and red. The probability that a pen is faulty depends on its colour. The probability of a faulty green pen is 0.1, while the probability of faulty blue and red pen is 0.15 and 0.08, respectively. In the box, 35% of the pens are green colour, 40% is blue colour and the rest is red colour. i) Draw a probability tree diagram to represent the above situation. (3 marks) ii) Calculate the probability of obtaining a non-faulty pen. (3 marks) iii) If a pen was found to be faulty, what is the probability that it is a green pen? (2 marks) b) The events M and Y are independent such that P(M) = a,P(Y) = 0.3. and P(M n Y) = 0.15. i) Find the value of a. (2 marks) ii) Find P(M U Y) and P(M'|Y'). (3 marks) c) How many 3 letter codes can be formed from the word 'SHOCK'? (2 marks)