(Solved): a) When Andrea needs a taxi, she rings one of three taxi companies, A, B or C. 50% of her calls ar ...

a) When Andrea needs a taxi, she rings one of three taxi companies, A, B or C. 50% of her calls are to taxi company A, 30% to B and 20% to C. A taxi from company A arrives late 4% of the time, a taxi from company B arrives late 6% of the time and a taxi from company C arrives late 17% of the time. (i) Draw a tree diagram to represent this information. (ii) Using your tree diagram, find the probability that, when Andrea rings for a taxi, it arrives late. (iii) Given that Andrea's taxi arrives late, find the conditional probability that she rang company B. b) The six digits 4, 5, 6, 7, 7, 7 can be arranged to give many different 6-digit numbers. (i) How many different 6-digit numbers can be made? (ii) How many of these 6-digit numbers start with an odd digit and end with an odd digit? c) A manufacturer makes two sizes of elastic bands: large and small. 40% of the bands produced are large bands and 60% are small bands. Assuming that each pack of these elastic bands contains a random selection, calculate the probability that, in a pack containing 20 bands, there are (i) equal numbers of large and small bands, (ii) more than 17 small bands.