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In a group of 24 actuaries, 20 have worked for Life Office A and 12 have worked for Life Office B. Everyone in the group has worked for at least one of the two companies. What is the probability that an actuary picked at random has worked for: (i) Life Office A and Life Office B (ii) Life Office A given that they have worked for Life Office B?The punctuality of trains has been investigated by considering a number of train journeys. In the sample, 60% of trains had a destination of Manchester, 20% Birmingham and 20% Edinburgh. The probabilities of a train arriving late in Manchester, Edinburgh or Birmingham are 30% , 20% and 25% respectively. If a late train is picked at random from the group under consideration, what is the probability that it terminated in Manchester