Download Worksheet 4.3

Maths Quest Maths A Year 12 for Queensland
WorkSHEET 4.3
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Chapter 4 Populations, samples, statistics and probability WorkSHEET 4.3
Probabilities
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Name: ___________________________
/50
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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}
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A bag contains 4 small coloured discs
coloured:
red
yellow
blue
green.
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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}
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Two coins are tossed. Calculate the probability
of tossing a Head and a Tail.
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S = {HH, HT, TH, TT}
2
P(H and T) 
4
1

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Maths Quest Maths A Year 12 for Queensland
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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.
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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}
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P( total is 7) 
36
1

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A coin is tossed and a die is rolled. Calculate
the probability of rolling an even number and
tossing a Head.
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S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4,
T5, T6}
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P(Head and even number) 
12
1

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Maths Quest Maths A Year 12 for Queensland
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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?
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 120
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 12
Number of ordered selections  20  19  18
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 6840
Number of arrangemen ts  3  2  1
6
Number of unordered selections  6840  6
 1140
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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
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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
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