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Maths Quest Maths A Year 12 for Queensland WorkSHEET 4.3 1 Chapter 4 Populations, samples, statistics and probability WorkSHEET 4.3 Probabilities 1 Name: ___________________________ /50 6 A small circular disc is coloured white on one side and black on the other. If the disc is tossed three times, draw a tree diagram and list the resulting sample space for the experiment. S = {bbb, bbw, bwb, bww, wbb, wbw, wwb, www} 2 A bag contains 4 small coloured discs coloured: red yellow blue green. 6 Two discs are removed from the bag one after the other (Note: the first disc is not returned). Draw a tree diagram and list the sample space for the experiment. S = {ry, rb, rg, yr, yb, yg, br, by, bg, gr, gy, gb} 3 Two coins are tossed. Calculate the probability of tossing a Head and a Tail. 6 S = {HH, HT, TH, TT} 2 P(H and T) 4 1 2 Maths Quest Maths A Year 12 for Queensland 4 Chapter 4 Populations, samples, statistics and probability WorkSHEET 4.3 Two dice are tolled. Find the probability that the total on the two dice is 7. 2 6 S = {1 and 1, 1 and 2, 1 and 3, 1 and 4, 1 and 5, 1 and 6, 2 and 1, 2 and 2, 2 and 3, 2 and 4, 2 and 5, 2 and 6, 3 and 1, 3 and 2, 3 and 3, 3 and 4, 3 and 5, 3 and 6, 4 and 1, 4 and 2, 4 and 3, 4 and 4, 4 and 5, 4 and 6, 5 and 1, 5 and 2, 5 and 3, 5 and 4, 5 and 5, 5 and 6, 6 and 1, 6 and 2, 6 and 3, 6 and 4, 6 and 5, 6 and 6} 6 P( total is 7) 36 1 6 5 A coin is tossed and a die is rolled. Calculate the probability of rolling an even number and tossing a Head. 6 S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6} 3 P(Head and even number) 12 1 4 Maths Quest Maths A Year 12 for Queensland 6 7 8 Chapter 4 Populations, samples, statistics and probability WorkSHEET 4.3 How many ways can five people be arranged in a line? Number of ways 5 4 3 2 1 There are four players in a squash team. In how many ways can a captain and vice-captain be chosen? Number of ways 4 3 From a class of 20 students, three are to be chosen to represent the class on the Student Representative Council. In how many ways can the three representatives be chosen? 3 4 120 4 12 Number of ordered selections 20 19 18 4 6840 Number of arrangemen ts 3 2 1 6 Number of unordered selections 6840 6 1140 9 10 The letters C, A and T are written on cards. The cards are shuffled, then laid face up in order. Calculate the probability that the cards spell the word CAT in correct order. A bag contains five marbles coloured red, yellow, green, blue and orange. Three marbles are selected from the bag. Calculate the probability that they are red, yellow and orange marbles. Note: they are not returned to the bag after selection. Number of arrangemen ts 3 2 1 4 6 Only one of these arrangements is in the correct order. 1 P(CAT) 6 Number of ordered selections 5 4 3 60 Number of arrangemen ts 3 2 1 6 Number of unordered arrangemen ts 60 6 10 P(red, yellow and orange 1 10 4