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Basic probability
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45 questions at your level
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Level 5
Probability of a single event
16 questions
Lesson
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A fair six-sided dice has faces numbered 1, 2, 3, 4, 5 and 6.
(a)
Write down the probability that the dice lands on a number greater than 4.
The dice is rolled 180 times.
(b)
Work out an estimate for the number of times the dice lands on a number greater than 4.
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Level 3
3 marks
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A bag contains only red beads, blue beads and green beads.
A bead is taken at random from the bag.
The probability that the bead is red is
3
x
3x
3
x
.
The probability that the bead is blue is
2
x
2x
2
x
.
The probability that the bead is green is
x
x
x
.
(a)
Work out the value of
x
x
x
.
(b)
Work out the probability that the bead is blue.
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Level 3
3 marks
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There are
30
30
30
students in a class.
18
18
18
of them are girls.
12
12
12
of the students wear glasses.
7
7
7
of the girls wear glasses.
A student is chosen at random. Work out the probability that the student is a boy who does not wear glasses. (3 marks)
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Level 3
3 marks
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There are only gold tokens, silver tokens, bronze tokens and copper tokens in a box.
Amir is going to take at random a token from the box.
The table shows the probability that he will take a gold token and the probability that he will take a silver token.
Token
gold
silver
bronze
copper
Probability
0.25
0.25
0.25
0.15
0.15
0.15
There are three times as many bronze tokens as copper tokens in the box.
(a)
Work out the probability that Amir will take a bronze token.
(3 marks)
There are
36
36
36
silver tokens in the box.
(b)
Work out the total number of tokens in the box.
(2 marks)
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Level 3
5 marks
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There are only green marbles, blue marbles and white marbles in a tin.
There are
18
18
18
white marbles in the tin.
Priya is going to take at random a marble from the tin.
The probability that the marble will be white is
0.15
0.15
0.15
number of green marbles : number of blue marbles
=
7
:
10
= 7 : 10
=
7
:
10
Work out the number of green marbles in the tin.
(4 marks)
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Level 3
4 marks
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Sample space & systematic listing
16 questions
Lesson
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Mark as done
Two fair six-sided dice are rolled and the two scores are added to give a total.
(a)
Find the probability that the total is
5
5
5
.
(b)
Find the probability that the total is at least
10
10
10
.
(c)
Jay says: "The total can be any whole number from
2
2
2
to
12
12
12
, so there are
11
11
11
possible outcomes and the probability of a total of
5
5
5
is
1
11
\frac{1}{11}
11
1
."
Explain why Jay is wrong.
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Level 3
5 marks
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Two fair six-sided dice are rolled. The score is the
positive difference
between the two numbers rolled. For example, a
6
6
6
and a
2
2
2
give a score of
4
4
4
, and a
3
3
3
and a
3
3
3
give a score of
0
0
0
.
(a)
Find the probability that the score is
1
1
1
.
(b)
Find the probability that the score is
3
3
3
or more.
(c)
Write down the most likely score, and explain how the sample space shows this.
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Level 3
6 marks
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Relative frequency & expected outcomes
14 questions
Lesson
Not started
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A spinner has four colours on it. Priya spins the spinner
60
60
60
times and records the colour it lands on.
Colour
Red
Blue
Green
Yellow
Frequency
24
15
9
12
\begin{array}{l|cccc}\text{Colour} & \text{Red} & \text{Blue} & \text{Green} & \text{Yellow} \\ \hline \text{Frequency} & 24 & 15 & 9 & 12\end{array}
Colour
Frequency
Red
24
Blue
15
Green
9
Yellow
12
(a)
Use Priya's results to estimate the probability that the spinner lands on green.
(b)
Priya spins the spinner a further
400
400
400
times. Estimate the number of times it lands on red.
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Level 3
4 marks
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Jamal rolls a dice
300
300
300
times. He rolls a six
72
72
72
times.
(a)
Work out the relative frequency of rolling a six.
(b)
Work out how many sixes Jamal would expect in
300
300
300
rolls if the dice were fair.
(c)
Do Jamal's results suggest that the dice is biased? Give a reason for your answer.
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Level 3
4 marks
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In a computer game, Leo attempts a level
80
80
80
times and completes it
28
28
28
times.
(a)
Use these results to estimate the probability that Leo completes the level on any one attempt.
(b)
Leo attempts the level
250
250
250
more times. Estimate the number of times he completes it.
(c)
Explain why your answer to part
(b)
cannot be the actual number of times Leo completes the level.
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Level 3
5 marks
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