b. "the students in a school Sixth torm were asked tor their most common mode or transport to school. The replies are summarised in the table below. Mode of transport I Walk/Cycle Public Private car Total _ _ _ transport _ _ Year 12 _ 44 _ 72 _ 16 132 Year Grmp Year 13 40 63 17 Total 84 135 33 252 (a) Two students are randomly selected. What is the probability that they are in different year groups? [2] (b) Two students are randomly selected. What is the probability that they are in different year groups but are in the same 'mode of transport' category? [3] (c) Based on the data given in the table, are the events 'in Year 12' and 'walk/eyele to school' independent? Clearly explain your reasoning. [3] 6. A practical music examination can be taken once or twice. Those candidates who fail it on the first occasion take it a second time. For those having their first attempt, 25% pass with distinction and 45% gain an ordinary pass. For those taking the examination for a second time, the corresponding figures are 5% and 70% respectively. The tree diagram below illustrates the situation