A box contains a large number of pens that are three colours: red, blue and green. The probability that a pen is faulty depends on its colour. The probability of a faulty red pen is 0.1. while the probability of faulty blue and green pens is 0.15 and 0.08, respectively. In the box, 35% of the pens is red in colour, 40% is blue in colour and the rest is green in colour.
(a) Draw the probability tree-diagram for this situation.
(b) Calculate the probability of obtaining a non-faulty pens.
(c) A pen is found to be faulty, what is the probability that it is a red pen?
(d) What is the probability of obtaining either a blue or green pen faulty?​