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Probability of a single event
16 questions
Lesson
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A biased four-sided spinner can land on 1, 2, 3 or 4.
The table shows information about the probability that the spinner lands on each number. The spinner is equally likely to land on 3 as it is to land on 4.
Number
1
2
3
4
Probability
0.15
0.35
y
y
y
y
y
y
(a)
Work out the value of
y
y
y
.
The spinner is spun 200 times.
(b)
Work out an estimate for the number of times the spinner lands on an even number.
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Level 4
6 marks
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Priya plays one game of chess each week. Each game she either wins, draws or loses.
The probability that Priya wins a game is
2
5
\frac{2}{5}
5
2
.
The probability that Priya draws a game is
15
%
15\%
15%
.
(a)
Work out the probability that Priya loses a game. Give your answer as a decimal.
(b)
Priya plays 60 games. Work out an estimate for the number of these games that Priya loses.
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Level 4
5 marks
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A bag contains only red counters and yellow counters.
There are 12 red counters in the bag.
A counter is taken at random from the bag. The probability that it is red is
0.3
0.3
0.3
.
(a)
Work out the total number of counters in the bag.
(b)
Work out the number of yellow counters in the bag.
A counter is taken at random, its colour is recorded, and the counter is put back in the bag. This is done 250 times.
(c)
Work out an estimate for the number of times a yellow counter is taken.
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Level 4
5 marks
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There are only
3
3
3
purple pens and
5
5
5
orange pens in a box.
Jay takes at random a pen from the box.
He records its colour and puts the pen back into the box.
Jay does this two more times.
Show that the probability that Jay takes at least two purple pens is
81
256
\frac{81}{256}
256
81
(4 marks)
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Level 4
4 marks
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Sample space & systematic listing
16 questions
Lesson
Not started
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A security code is made from one letter chosen from A, B, C, D, followed by two digits, each chosen from
0
0
0
to
9
9
9
.
For example, C07 is a possible code.
(a)
Work out how many different codes are possible.
(b)
Work out how many of these codes have two digits that are different from each other.
(c)
One of the codes from part
(a)
is chosen at random. Find the probability that it ends in
00
00
00
.
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Level 4
6 marks
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A club has six members: Ana, Ben, Cal, Dee, Eve and Femi.
(a)
Two of the six members are chosen to go to a conference together. Work out how many different pairs could be chosen.
(b)
Instead, one of the six is chosen as chairperson and a different one is chosen as secretary. Work out how many different ways this can be done.
(c)
Explain how the answer to part
(b)
is related to the answer to part
(a)
.
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Level 4
4 marks
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A fair six-sided die numbered
1
1
1
to
6
6
6
is rolled, and a fair four-sided spinner numbered
1
1
1
,
2
2
2
,
3
3
3
and
5
5
5
is spun.
The number on the die is multiplied by the number on the spinner to give the score.
(a)
Work out how many equally likely outcomes there are.
(b)
Find the probability that the score is an odd number.
(c)
Find the probability that the score is greater than
20
20
20
.
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Level 4
5 marks
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Each sandwich at a sandwich bar is made with one type of bread, one filling and one sauce.
There are
4
4
4
types of bread.
There are
9
9
9
fillings.
There are
x
x
x
sauces.
There are
252
252
252
different ways to choose one type of bread, one filling and one sauce.
Work out the value of
x
x
x
.
(2 marks)
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Level 4
2 marks
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There are
11
11
11
runners in a junior race.
One runner wins a gold medal.
A different runner wins a silver medal.
There are
14
14
14
runners in a senior race.
One runner wins a gold medal.
A different runner wins a silver medal.
Work out how many different ways these four medals can be won.
(3 marks)
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Level 4
3 marks
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Relative frequency & expected outcomes
14 questions
Lesson
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Ann and Ben each test the same spinner.
Ann spins it
50
50
50
times and it lands on green
18
18
18
times.
Ben spins it
150
150
150
times and it lands on green
42
42
42
times.
(a)
Use
all
of their results to estimate the probability that the spinner lands on green.
(b)
Chloe says the best estimate is the mean of Ann's and Ben's relative frequencies, which is
0.32
0.32
0.32
. Explain why Chloe's method does not give the best estimate.
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Level 4
3 marks
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A spinner can land on red, blue or white. Nadia spins the spinner a number of times. The relative frequency of red is
0.28
0.28
0.28
, and the spinner landed on red
63
63
63
times.
(a)
Work out how many times Nadia spun the spinner.
(b)
The spinner landed on blue
90
90
90
times. Use Nadia's results to estimate the probability that the spinner lands on white.
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Level 4
4 marks
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A spinner has five equal sections numbered
1
1
1
to
5
5
5
. Priya spins it
500
500
500
times, working out the relative frequency of a
1
1
1
as she goes.
Number of spins
10
20
50
100
200
500
Relative frequency of a
1
0.3
0.25
0.22
0.21
0.205
0.202
\begin{array}{l|cccccc}\text{Number of spins} & 10 & 20 & 50 & 100 & 200 & 500 \\ \hline \text{Relative frequency of a }1 & 0.3 & 0.25 & 0.22 & 0.21 & 0.205 & 0.202\end{array}
Number of spins
Relative frequency of a
1
10
0.3
20
0.25
50
0.22
100
0.21
200
0.205
500
0.202
(a)
Which of Priya's figures is the best estimate of the probability of spinning a
1
1
1
? Give a reason for your answer.
(b)
Do Priya's results suggest the spinner is fair? Explain your answer.
(c)
A different spinner also has five equal sections numbered
1
1
1
to
5
5
5
, and is known to be fair. Estimate the number of
1
1
1
s in
3000
3000
3000
spins of this spinner.
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Level 4
6 marks
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A biased spinner has five sections numbered
1
1
1
,
2
2
2
,
3
3
3
,
4
4
4
and
5
5
5
Leah spins the spinner
80
80
80
times.
The table gives the number of times the spinner lands on each number.
Number
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
Frequency
14
14
14
20
20
20
11
11
11
19
19
19
16
16
16
Leah is going to spin the spinner two more times.
(a)
Work out an estimate for the probability that the spinner will land on
4
4
4
both times.
(3 marks)
Marcus will spin the same spinner
n
n
n
times and use his results to get a better estimate of this probability.
(b)
What can you say about the value of
n
n
n
?
(1 mark)
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Level 4
4 marks
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