Maths Quest Maths A Year 12 for Queensland Chapter 4 Populations, samples, statistics and probability WorkSHEET 4.3 1

WorkSHEET 4.3 Probabilities Name: ______

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1  / 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} / 6
2  / A bag contains 4 small coloured discs coloured:
red
yellow
blue
green.
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} / 6
3  / Two coins are tossed. Calculate the probability of tossing a Head and a Tail. /
S = {HH, HT, TH, TT}
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4  / Two dice are tolled. Find the probability that the total on the two dice is 7. / S = {1 and 1, 1 and 2, 1 and 3, 1 and 4, 1and5, 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}
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5  / A coin is tossed and a die is rolled. Calculate the probability of rolling an even number and tossing a Head. /
S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
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6  / How many ways can five people be arranged in a line? / / 4
7  / There are four players in a squash team. In how many ways can a captain and vice-captain be chosen? / / 4
8  / 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? / / 4
9  / 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. /
Only one of these arrangements is in the correct order.
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10  / 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. / / 4