QUESTION 5 a) 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 0.03. 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) o Halt Cip'tl Unlvmitt Toknologl MAM CONFIDENTIAL CONFIDENTIAL E CSiFEB2022iQMT181lSTA104 b) The events M and Y are independent such that HM) = a,P(Y) = 0.3, and P(M n Y) = 0.15. l) Find the value of o. (2 marks) ii) Find P(M U 1') and P(M'|Y'). (3 marks) 0) How many 3 letter codes can be formed from the word 'SHOCK'? (2 marks)