There are 6 balls in an urn, of which 4 balls are red and 2 balls are blue. You do the following: • draw a ball from the urn at random, note its colour, do not return the ball to the urn; • draw a second ball, note its colour, do not return the ball to the urn; • finally draw a third ball and note its colour. (i) Describe the corresponding discrete probability space (Ω, F, P). [25 Marks] (ii) Consider the following event, A: Exactly two of the balls are red. Write down A as a subset of the sample space Ω and find its probability, P(A).

Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month, a Brand A user has a 20 probability of switching to Brand B and a 5 of not using either brand. A Brand B user has a 15 probability of switching to Brand A and a 10 probability of not using either brand. A nonuser has a 10 probability of purchasing Brand A and a 15 probability of purchasing Brand B. How many people will be in each group a in 1 month, b in 2 months, and c in 18 months?

Smokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one pack or less per day. During any month, there is a 5 probability that a nonsmoker will begin smoking a pack or less per day, and a 2 probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10 probability of quitting and a 10 probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 5 probability of quitting and a 10 probability of dropping to a pack or less per day. How many people will be in each group a in 1 month, b in 2 months, and c in 1 year?