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M_BANK\YR11-GEN\PROBABILITY02.HSC
Relative Frequency and Probability
1)!
2)!
MIS86-B9iii
A pack of cards consists of 52 cards in 4 suits and within each suit there are 13 cards in
ascending order of value 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace.
Two players A and B play a game in which they are dealt one card each at random from the
same pack. The higher value card wins. A shows his card first and it is a Jack. What is the
probability of B drawing
a.
a higher value card?
b.
a lower value card?
c.
another Jack?¤
4
12
1
« a)
b)
c)
»
17
17
17
MIS88-A3a
B
A
C
Fail
D
3)!
4)!
E
In a certain skills test candidates were given the grades A, B, C, D, or FAIL. The sector
graph, which is divided up into 100 parts, shows the distribution of 240 candidates in this
skills test.
i.
What percentage of candidates failed?
ii.
How many candidates were given a grade E?
iii.
What is the probability that a candidate, selected at random, was given either a
grade A or a grade B?¤
« i) 5% ii) 36 iii) 0·3 »
MIS89-B9a
Five people A, B, C, D and E turn up to play squash.
i.
List all possible ways two people can be chosen to play first.
ii.
What is the probability that D plays in the first game?
iii.
What is the probabilty that B and C play first?¤
« i) AB, AC, AD, AE, BC, BD, BE, CD, CE, DE ii) 2 iii) 1 »
10
5
MIS91-A3c
The wheel shown is spun around until it stops on a number.
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1
4
7
6
10
8
3
5
11
9
12
5)!
6)!
7)!
8)!
9)!
2
Given that the wheel is equally likely to stop on any number, find the probability that the
wheel stops on:
i.
12;
ii.
a number divisible by 5.¤
1
1
« i)
ii) »
12
6
MIS91-A4a
In a board game the number of squares that a counter is moved is the number shown after
throwing an ordinary six-sided die.
i.
What is the probability of throwing a six with a single throw of the die?
ii.
In this board game, some squares are shaded. A counter is shown on the first
square.
What is the probability that the counter finishes on a shaded square when the die is
thrown once?¤
1
1
« i) ii) »
6
3
MIS92-A5a
A bag contains 15 black, 35 red, and 25 green jelly beans. If one jelly bean is selected at
random, what is the probability of selecting a black jelly bean?¤
« 1 »
5
MIS93-A18
A coin is tossed three times. What is the probability that the side showing on the last toss is
the same as that showing on the first toss?
(A) 1
(B) 1
(C) 3
(D) 1 ¤
8
8
4
2
« D »
MIS94-A3
Ronald has a jar which contains 100 jellybeans: 50 red, 40 white, and 10 black. He takes out
the black jellybeans, and offers the jar to Nancy to choose a jellybean at random. What is the
probability that Nancy chooses a white jellybean?
(A) 1
(B) 2
(C) 4
(D) 4 ¤
5
5
2
9
« D »
MIS95-A5
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$
10)!
11)!
In a game show there are nine boxes, three of which contain money. All the other boxes are
empty. Two boxes have already been chosen as shown ($ = money). What is the probability
that the next box chosen holds a money prize?
1
1
2
2
(A)
(B)
(C)
(D)
¤
9
7
4
3
« C »
MIS99-2
An unbiased coin is tossed three times. On the first two tosses the result is heads. What is
the probability that the result of the third toss will be a head?
1
1
1
1
(A)
(B)
(C)
(D) ¤
8
6
4
2
« D »
GEN01-7
Brenda surveyed the students in her year group and summarised the results in the following
table.
Play tennis
Right-handed
Left-handed
TOTALS
12)!
13)!
no
prize
Do not play
tennis
81
29
110
53
22
75
TOTALS
134
51
185
What percentage of the left-handed students in this group play tennis? (Round your answer
to the nearest whole number.)
(A) 11%
(B) 12%
(C) 29%
(D) 43%
«D »
GEN02-20
Rob, Alex and Tan plan a swimming race against each other. Rob and Alex are each twice as
likely as Tan to win the race. What is the probability that Tan will win the race?
1
1
1
1
(A)
(B)
(C)
(D) ¤
6
5
4
3
« B »
GEN02-24
a.
Jane and Sam are in a Geography class of 12 students. The class is going on a
three-day excursion by bus. The students are asked to each pack one bag for the
trip. The bags are weighed, and the weights (in kg) are listed on order as follows:
8, 9, 10, 10, 15, 18, 22, 25, 29, 35, 38, 41.
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i.
b.
A bag is selected at random. What is the probability that the chosen bag
weighs more than 30 kg?
ii.
While Sam waits for the bus to be ready, he works out the five number
summary for the weight of the bags: 8, 10, 20, 32, 41. Using this five
number summary, construct an accurate box-and-whisker plot to display
the distribution of the weights of the bags.
iii.
Calculate the interquartile range of the weights.
While waiting in the carpark, Jane notices that some of the cars entering the carpark
have headlights on. For each car, Jane notes whether or not the lights are on, and
whether the driver is male or female. Her results are represented in the two-way
table below. There are two missing numbers at A and B.
Male drivers
Female drivers
Total
c.
« a) i)
Headlights on
10
8
B
Headlights off
A
62
105
i.
Determine the values of A and B.
ii.
How many cars are included in this data set?
iii.
What fraction of the cars had female drivers?
iv.
Of the cars driven by women, what fraction had headlights on?
There is one seat at the back of the excursion bus that is very popular among the
students. Before the excursion, a draw is conducted to determine who will sit in the
popular seat. The names of the 12 students are placed in a hat and 3 names are
drawn without replacement. The first name drawn determines who will sit in the
seat on the first day. The second name drawn determines who will sit in the seat on
the second day. The third name determines who will sit in the seat on the third day.
i.
What is the probability that Jane’s name is the first drawn?
ii.
What is the probability that Jane’s name is the second drawn?
iii.
What is the probability that Jane’s name will NOT be one of the three
names drawn from the hat? ¤
1
ii)
4
0
8 10
20
30 32
40 41
50
iii)
14)!
Total
53
70
iii) 22 b) i) A = 43, B = 18 ii) 123
70
4
3
1
1
iv)
c) i)
ii)
iii) »
123
35
4
12
12
GEN03-13
Joy asked the Students in her class how many brothers they had. The answers were recorded
in a frequency table as follows:
Number of brothers
0
1
2
3
Frequency
5
10
3
1
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4
15)!
1
One of the students is chosen at random. What is the probability that this student has at least
two brothers?
(A) 010
(B) 015
(C) 025
(D) 075¤
«C »
GEN03-22
Charlie surveyed 12 school friends to find out their preferences for chocolate. They were
asked to indicate their liking for milk chocolate on the following scale.
Dislike
Like
strongly moderately a little a little moderately strongly
0
1
2
3
4
5
They were also asked to do this for dark chocolate. Charlie displayed the results in a
spreadsheet and graph as shown below.
16)!
Charlie assumes that these 12 students are representative of the 600 students at the school.
What is Charlie’s estimate of the number of students in the school who like milk chocolate
but dislike dark chocolate?
(A) 50
(B) 200
(C) 250
(D) 450¤
«C »
GEN03-27a
A Celebrity mathematician, Karl arrives in Sydney for one of his frequent visits. Karl is
known to stay at one of three Sydney hotels. Hotel X is his favourite, and he stays there on
50% of his visits to Sydney. When he does not stay at Hotel X, he is equally likely to stay at
Hotels Y or Z.
i.
What is the probability that he will stay at Hotel Z?
ii.
On his first morning in Sydney, Karl always flips a coin to decide if he will have a
cold breakfast or hot breakfast. If the coin comes up heads he has a cold breakfast.
If the coin comes up tails he has a hot breakfast.
1. List all the possible combinations of hotel and breakfast choices.
2. Give a brief reason why these combinations are not all equally likely.
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3. Calculate the probability that Karl stays at Hotel Z and has a cold breakfast. ¤
1
ii) 1) X/cold, X/hot, Y/cold, Y/hot, Z/cold, Z/hot 2) The choice of hotels is not equally likely
4
1
3) »
8
17)! GEN04-1
Which fraction is equal to a probability of 25% ?
1
1
1
1
(A)
(B)
(C)
(D) ¤
25
4
3
2
« B »
18)! Gen05-3
Four radio stations reported the probability of rain as shown in the table.
« i)
Radio Station
2AT
2BW
2CZ
Probability of rain
053
17%
13
25
06
2DL
Which radio station reported the highest probability of rain?
(A) 2AT
(B) 2BW
(C) 2CZ
(D) 2DL¤
« D »
19)!
Gen05-11
The diagram shows a spinner.
2
4
7
7
9
20)!
1
The arrow is spun and will stop in one of the six sections. What is the probability that the
arrow will stop in a section containing a number greater than 4?
2
2
1
1
(A)
(B)
(C)
(D) ¤
5
3
3
2
« D »
Gen05-23a
There are 100 tickets sold in a raffle. Justine sold all 100 tickets to five of her friends. The
number of tickets she sold to each friend is shown in the table.
Friend
Danielle
Khalid
Nancy
Number of tickets
45
5
10
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Shani
Herman
Total
14
26
100
i.
Justine claims that each of her friends is equally likely to win first prize. Give a
reason why Justine’s statement is NOT correct.
ii.
What is the probability that first prize is NOT won by Khalid or Herman?¤
« i) Each of Justine’s friends bought a different number of tickets. The person with a higher
69
number of tickets will have a higher chance of winning. ii)
»
100
21)! Gen06-10
Kay randomly selected a marble from a bag of marbles, recorded its colour and returned it to
the bag. She repeated this process a number of times.
Colour
22)!
Tally
Frequency
Red
7
Blue
3
Yellow
2
Green
4
Purple
8
Based on these results, what is the best estimate of the probability that Kay will choose a
green marble on her next selection?
5
1
1
1
(A)
(B)
(C)
(D) ¤
24
24
6
5
« C »
Gen06-25a
Three cards labelled C, J, and M can be arranged in any order.
eg.
i.
ii.
iii.
M
C
J
In how many different ways can the cards be arranged?
What is the probability that the second card in an arrangement is a J?
What is the probability that the last card in an arrangement is not a C?¤
« i) 6 ii)
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1
2
iii) »
3
3