Download Worksheet 13.2 Answers - Maths and Science at Al Siraat

WorkSHEET 13.2
1
Probability II
Name: ___________________________
Which of the following are equally likely
events?
Estimate the probability of each event.
(a)
Getting a Head when tossing 1 coin.
(a)
(b)
Getting at least one Head when tossing
2 coins.
Getting a 3 when tossing a single die.
(b)
(d)
Getting an even number when tossing a
single die.
(d)
(e)
Getting 1 Head and 1 Tail when tossing
2 coins.
(e)
(c)
(c)
1
or 0.5
2
3
4
1
6
1
or 0.5 (that is, tossing a 2, 4 or 6)
2
1
or 0.5 (that is, HT or TH)
2
Therefore events (a), (d) and (e) are equally
likely.
2
3
A card is drawn from a standard deck. Find the
probability of each of the following:
(a)
(a) selecting an ace
1
4
=
52 13
1
13
P(spade) =
=
52
4
P(ace) =
(b)
selecting a spade
(b)
(c)
selecting the ace of spades
(c)
P(ace of spades) =
(d)
selecting a black ace
(d)
P(black ace) =
(e)
selecting a black picture card.
(e)
P(black picture card) =
The heights (in cm) of a class of Year 9
students are recorded in the following table.
Height
Number
150 152 154 156 158 160 162
2
3
5
4
3
0
1
Find the probability that a student is between
153 and 159 cm tall.
1
52
1
2
=
52
26
3
6
=
52
26
Total number of students
=2+3+5+4+3+0+1
= 18
Number between 153 and 159
=5+4+3
= 12
12
18
2
=
3
P(between 153 and 159) =
© John Wiley & Sons Australia, Ltd 2012
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4
Using the data from question 3, what could you Determine the proportion of students who are
say about the number of Year 9 students who
shorter than 151 cm.
are shorter than 151 cm in a school where there
2
P(shorter
than
151
cm)
=
are 198 Year 9 students in total?
18
1
=
9
E(x) = expected value
n = number of students
p = probability that a student is shorter than
151 cm
E(x) = n  p
E(no. students < 151 cm) = 198 
1
9
= 22
Therefore approximately 22 students are
expected to be shorter than 151 cm.
5
6
A pharmacy is able to fill the prescriptions for
19
of its customers. If the pharmacy expects
20
300 customers today, how many prescriptions
can it expect to fill?
Consider the following table that shows the
number of different brands of mobile phones
owned by males and females in a youth group.
Males Females
Apple
56
120
Nokia
34
148
Sony
12
136
Samsung
10
108
LG
68
224
E(x) = n  p
19
20
= 285 prescriptions
E(no. of prescriptions) = 300 
Total number of mobiles = 916
Total number of Samsung mobiles
= 10 + 108
= 118
118
916
59
=
( 0.1288)
458
Relative frequency =
Determine the relative frequency of Samsung
mobiles in the group.
© John Wiley & Sons Australia, Ltd 2012
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Using the data from question 6, a mobile gets
From the previous question there were
lost at the rate of 1 per day. If this mobile can
916 mobiles in total.
be considered to be randomly selected from the
entire group, what is the probability that the
Of these, 34 are Nokia phones owned by males.
phone that is lost is a Nokia phone owned by a
male?
34
P(Nokia owned by male) =
916
17
=
458
 0.0371
8
At a football match 20 Collingwood supporters
were asked what other team they disliked most.
Their responses were:
 18 said Carlton
 12 said Essendon.
If 18 said Carlton, 12 said Essendon and only
20 were surveyed then 10 must have replied
with both Carlton and Essendon.
Draw the Venn diagram with two intersecting
circles labelled Carlton and Essendon.
Show this information in a Venn diagram.
Place 10 in the intersection.
Place 8 in Carlton only.
Place 2 in Essendon only.
9
A Collingwood supporter is chosen at random.
Based on the Venn diagram in question 8. What
is the probability that this supporter:
(a) dislikes both Carlton and Essendon?
(b)
(c)
10 1

20 2
(a)
P(Both) 
(b)
P(Carlton only) 
dislikes only Carlton?
dislikes Essendon?
(c)
8 2

20 5
12 3

P(Essendon) 
20 5
© John Wiley & Sons Australia, Ltd 2012
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10
Mr Venn is a mathematics teacher who asks
each student in his class if they study
geography, history or economics. Here is the
data that Mr Venn gathered.
 10 study geography only
 5 study history only
 8 study economics only
 1 studies all three subjects
 3 study geography and history only
 7 study geography and economics only
 None study economics and history only
(a)
Display the information in a Venn
diagram.
(b)
Use the diagram to determine the number
of students from Mr Venss’s maths class
in each of the three classes.
(c)
How many students are in Mr Venn’s
mathematics class?
(a)
Draw a rectangle with three intersecting
circles and place the figures in the
corresponding sections.
(b)
Adding the numbers in each circle
Geography = 21
History = 9
Economics = 16
(c)
Adding all numbers in the Venn diagram
gives a total of 34 students in Mr Venn’s
mathematics class.
© John Wiley & Sons Australia, Ltd 2012
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