Probability Toolkit (Cambridge O Level Maths)

Exam Questions

2 hours43 questions
1
Sme Calculator
1 mark

A box contains 3 blue pens, 4 red pens and 8 green pens only.
A pen is chosen at random from the box.

Find the probability that this pen is green.

Did this page help you?

2
Sme Calculator
1 mark

Samira has a bag containing 20 sweets.
In the bag, there are 5 red, 6 green and 9 yellow sweets.

Samira chooses one sweet at random from the bag.

Write down the probability that she chooses a yellow sweet.

Did this page help you?

3
Sme Calculator
2 marks

The probability that a biased dice will land on a five is 0.3

Megan is going to roll the dice 400 times.

Work out an estimate for the number of times the dice will land on a five.

Did this page help you?

4a
Sme Calculator
1 mark

Jane has a packet of seeds.
The probability that a seed will grow is 0.75

What is the probability that a seed will not grow?

4b
Sme Calculator
2 marks

Jane plants 200 of these seeds.

Estimate the number of the seeds that will grow.

Did this page help you?

5
Sme Calculator
3 marks

cie-igcse-2020-oct-nov-p4-tz2-q6a

The diagram shows six discs.
Each disc has a colour and a number.

One disc is picked at random.

Write down the probability that

i)
the disc has the number 4,

[1]
ii)
the disc is red and has the number 3,
 
[1]
iii)
the disc is blue and has the number 4.
 
[1]

Did this page help you?

6
Sme Calculator
1 mark

The heights, metres, of the 120 boys in an athletics club are recorded.
The table shows information about the heights of the boys.

Height

(h metres)

1.3 less than h less or equal than 1.4 1.4 less than h less or equal than 1.5 1.5 less than h less or equal than 1.6 1.6 less than h less or equal than 1.7 1.7 less than h less or equal than 1.8 1.8 less than h less or equal than 1.9
Frequency 7 18 30 24 27 14

One boy is chosen at random from the club.

Find the probability that this boy has a height greater than 1.8 m.

Did this page help you?

7
Sme Calculator
1 mark

The test scores of 14 students are shown below.

21 21 23 26 25 21 22 20 21 23 23 27 24 21

A student is chosen at random.
 
Find the probability that this student has a test score of more than 24.

Did this page help you?

8
Sme Calculator
1 mark

20 students each record the mass, p grams, of their pencil case.
The table below shows the results.

Mass
(p grams)
0 less than p less or equal than 50 50 less than p less or equal than 100 100 less than p less or equal than 125 125 less than p less or equal than 150 150 less than p less or equal than 200
Frequency 2 5 4 6 3

A student is chosen at random.
 
Find the probability that this student has a pencil case with a mass greater than 150 g.

Did this page help you?

9a
Sme Calculator
2 marks

Maya has a spinner with four sections numbered 1 to 4.

She spins the spinner 200 times.
Her results are shown in the table.

Number on spinner 1 2 3 4
Frequency 25 70 55 50

i)
Write down the relative frequency of the spinner landing on 2.

[1]

ii)
Maya says that this relative frequency is a good estimate for the probability of the spinner landing on 2.

Explain why she is correct.
[1]
9b
Sme Calculator
1 mark

Maya spins the spinner 500 times.

Find the number of times Maya should expect the spinner to land on 2.

Did this page help you?

10
Sme Calculator
1 mark

In a survey, 3 out of every 100 women were taller than 1.9 m.
One of these 100 women is picked at random.

Calculate the probability that she is not taller than 1.9 m.

Did this page help you?

11a
Sme Calculator
1 mark

A machine puts beads of different colours and sizes into packets.
The beads are selected at random from a large container and the selection of each bead for a packet is independent of all others.
The table shows information on the contents of six packets.

Packet 1 2 3 4 5 6 Total
Total number of beads 15 14 19 18 16 18 100
Number of blue beads 6 5 8 6 8 7  

Calculate the relative frequency of the machine selecting a blue bead.

11b
Sme Calculator
1 mark

Calculate how many blue beads you would expect in a packet of 30 beads.

11c
Sme Calculator
1 mark

The probability that the machine selects a red bead is 0.17.

Calculate the probability that the machine does not select a red bead.

Did this page help you?

1a
Sme Calculator
2 marks

A bag contains blue, red, yellow and green balls only.
A ball is taken from the bag at random.
The table shows some information about the probabilities.

 Colour Blue Red Yellow Green
 Probability 0.15 0.2   0.43


Complete the table.

1b
Sme Calculator
1 mark

Abdul takes a ball at random and replaces it in the bag.
He does this 200 times.

Find how many times he expects to take a red ball.

Did this page help you?

2
Sme Calculator
2 marks

A group of 200 people were asked which city they would like to visit next.
The table shows the results.

City London Paris New York Tokyo
Number of people 50 48 56 46

 
A person from the group is chosen at random.
 
Write down the probability that this person would like to visit either Paris or Tokyo next.

Did this page help you?

3a
Sme Calculator
2 marks

There are only red counters, blue counters, white counters and black counters in a bag.

The table shows the probability that a counter taken at random from the bag will be red or blue.

Colour red blue white black
Probability 0.2 0.5    

The number of white counters in the bag is the same as the number of black counters in the bag.

Tania takes at random a counter from the bag.

Work out the probability that Tania takes a white counter.

3b
Sme Calculator
2 marks

There are 240 counters in the bag.

Work out the number of red counters in the bag.

Did this page help you?

4
Sme Calculator
1 mark

Tanya plants some seeds.
When a seed produces flowers, the probability that the flowers are red is 0.6 and the probability that the flowers are yellow is 0.3.

Tanya has a seed that produces flowers.
 
Find the probability that the flowers are not red and not yellow.

Did this page help you?

5
Sme Calculator
2 marks

Suleika has six cards numbered 1 to 6.

cie-igcse-2020-march-p4-tz2-q6a

She takes one card at random, records the number and replaces the card.

i)
Write down the probability that the number is 5 or 6.


[1]

ii)
Suleika does this 300 times.

Find how many times she expects the number 5 or 6.


[1]

Did this page help you?

6
Sme Calculator
2 marks

cie-igcse-2019-oct-nov-p4-tz1-q8

The diagram shows 5 cards.

Donald chooses a card at random.

i)
Write down the probability that the number of dots on this card is an even number.

[1]

ii)
Write down the probability that the number of dots on this card is a prime number.

[1]

Did this page help you?

7a
Sme Calculator
3 marks

Here is a four sided spinner.
The spinner is biased.

q4-1-5-medium-edexcel-gcse-maths

The table shows the probabilities that the spinner will land on 1 or on 3

Number 1 2 3 4
Probability 0.2   0.1  


The probability that the spinner will land on 2 is the same as the probability that the spinner will land on 4

Work out the probability that the spinner will land on 4.

7b
Sme Calculator
2 marks

Shunya is going to spin the spinner 200 times.

Work out an estimate for the number of times the spinner will land on 3.

Did this page help you?

8
Sme Calculator
3 marks

Carol spins a spinner 80 times.

The table shows information about her results.

Outcome Frequency
J 39
K 25
L 16



Dan spins this spinner 300 times.

Work out an estimate for the number of times that Dan will get an L.

Did this page help you?

9
Sme Calculator
3 marks

A new housing estate is being planned.
There are three possible plans: A comma space B and C.
A survey was carried out to see which plan people preferred.
The relative frequency table shows the results.

Plain A B C
Relative Frequency 0.3 0.5 0.2

52 people preferred plan C.

i)
Find how many people preferred plan A.

[2]
ii)
Calculate the total number of people surveyed.
[1]

Did this page help you?

1
Sme Calculator
2 marks

Bill has some counters in a bag.

3 of the counters are red.
7 of the counters are blue.
The rest of the counters are yellow.

Bill takes at random a counter from the bag.

The probability that he takes a yellow counter is 2 over 7

How many yellow counters are in the bag before Bill takes a counter?

Did this page help you?

2a
Sme Calculator
2 marks

Karl wants to raise money for charity.
He designs a game for people to play.

Karl uses a fair 10-sided dice for the game.
The dice is numbered from 1 to 10

Each person will roll the dice once.
A person wins the game if the dice lands on a multiple of 4

Ali plays the game once.

Work out the probability that Ali will win the game.

2b
Sme Calculator
3 marks

Each person pays 30p to play the game once.
The prize for a win is £1

Karl thinks that the game will be played 100 times.

Work out an estimate for how much money Karl will raise for charity.

Did this page help you?

3
Sme Calculator
3 marks

There are only blue cubes, yellow cubes and green cubes in a bag.

There are

  twice as many blue cubes as yellow cubes
and  four times as many green cubes as blue cubes.


Hannah takes at random a cube from the bag.

Work out the probability that Hannah takes a yellow cube.

Did this page help you?

4a
Sme Calculator
1 mark

There are only blue counters, yellow counters, green counters and red counters in a bag.
A counter is taken at random from the bag.

The table shows the probabilities of getting a blue counter or a yellow counter or a green counter.

Colour blue yellow green red
Probability 0.2 0.35 0.4  


Work out the probability of getting a red counter.

4b
Sme Calculator
2 marks

What is the least possible number of counters in the bag?
You must give a reason for your answer.

Did this page help you?

5
Sme Calculator
3 marks

There are only red counters, blue counters and purple counters in a bag.
The ratio of the number of red counters to the number of blue counters is 3 : 17

Sam takes at random a counter from the bag.
The probability that the counter is purple is 0.2

Work out the probability that Sam takes a red counter.

Did this page help you?

6
Sme Calculator
3 marks

There are 5 girls, 6 boys and some adults in a room.
Jenny selects at random one of these people.

The probability that Jenny selects a girl is 1 third

Work out the probability that Jenny selects an adult.

Did this page help you?

7a
Sme Calculator
2 marks

There are 54 fish in a tank.
Some of the fish are white and the rest of the fish are red.

Jeevan takes at random a fish from the tank.
The probability that he takes a white fish is 4 over 9

Work out the number of white fish originally in the tank.

7b
Sme Calculator
2 marks

Jeevan puts the fish he took out, back into the tank.
He puts some more white fish into the tank.

Jeevan takes at random a fish from the tank.
The probability that he takes a white fish is now 1 half

Work out the number of white fish Jeevan put into the tank.

Did this page help you?

8
Sme Calculator
4 marks

There are 90 counters in a bag.
Each counter in the bag is either red or blue so that

the number of red counters : the number of blue counters = 2 space colon space 13

Li is going to put some more red counters in the bag so that

the probability of taking at random a red counter from the bag is 1 third

Work out the number of red counters that Li is going to put in the bag.

Did this page help you?