1. Probability – Mixed – Higher – GCSE Questions – AQA
These questions are the same format as previous GCSE exams.
COPY means they use the exact same numbers as the original GCSE question.
Otherwise, they are clone questions using different numbers.
The worksheets are provided in 2 sizes.

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3. AQA Higher: June 2017 Paper 2, Q5 AQA Higher: June 2017 Paper 2, Q5
A code has 4 digits.
Each digit is a number from 0 to 9
Digits may be repeated.
The code starts 9 8 5 1
A code has 4 digits.
Each digit is a number from 0 to 9
Digits may be repeated.
The code starts 9 8 5 9 8 5 9 8 5
[1 mark]
[1 mark]
1 (a)
Alice chooses a number at random for the last digit.
Write down the probability that she chooses the correct number.
1 (a)
Alice chooses a number at random for the last digit.
Write down the probability that she chooses the correct number.
Answer
Answer
1 (b)
[1 mark]
[1 mark]
Trevor knows the last digit is odd but not 1 or 9.
He chooses a different odd number at random.
What is the probability that he chooses the correct number?.
1 (b)
Trevor knows the last digit is odd but not 1 or 9.
He chooses a different odd number at random.
What is the probability that he chooses the correct number?.
Answer
Answer

5. AQA Higher: June 2017 Paper 3, Q9 AQA Higher: June 2017 Paper 3, Q9
There are 660 boys and 840 girls in a school.
The probability that a boy chosen at random studies Drama is 2 5
The probability that a girl chosen at random studies Drama is 3 7 1
There are 660 boys and 840 girls in a school.
The probability that a boy chosen at random studies Drama is 2 5
The probability that a girl chosen at random studies Drama is 3 7
1 (a)
Work out the number of students in the school who study Drama.
1 (a)
Work out the number of students in the school who study Drama.
[3 marks]
[3 marks]
Answer
Answer
1 (b)
Work out the probability that a student chosen at random
from the whole school does not study Drama.
1 (b)
Work out the probability that a student chosen at random
from the whole school does not study Drama.
[2 marks]
[2 marks]
Answer
Answer

7. AQA Higher: November 2017 Paper 1, Q15
Meal Deal
Choose one sandwich, one drink and one snack
Meal Deal
Choose one sandwich, one drink and one snack
There are
8 different sandwiches
4 different drinks
and
5 different snacks.
There are
8 different sandwiches
4 different drinks
and
5 different snacks.
1 (a)
How many different Meal Deal combinations are there?
1 (a)
How many different Meal Deal combinations are there?
[2 marks]
[2 marks]
Answer
Answer
1 (b)
Three of the sandwiches have cheese in them.
Two of the drinks are fizzy.
Eva picks a Meal Deal at random.
Work out the probability that the sandwich has cheese in it
and the drink is fizzy.
Give your answer as a fraction.
1 (b)
Three of the sandwiches have cheese in them.
Two of the drinks are fizzy.
Eva picks a Meal Deal at random.
Work out the probability that the sandwich has cheese in it
and the drink is fizzy.
Give your answer as a fraction.
[2 marks]
[2 marks]
Answer
Answer

9. AQA Higher: June 2018 Paper 3, Q27 AQA Higher: June 2018 Paper 3, Q27
A bag contains 30 discs.
10 are red and 20 are blue.
One disc is taken out at random and replaced by
two of the other colour.
Another disc is then taken out at random and replaced by
Another disc is then taken out at random.
Work out the probability that all three discs taken out are red. 1
A bag contains 30 discs.
10 are red and 20 are blue.
One disc is taken out at random and replaced by
two of the other colour.
Another disc is then taken out at random and replaced by
Another disc is then taken out at random.
Work out the probability that all three discs taken out are red.
[3 marks]
[3 marks]
Answer
Answer

11. AQA Higher: November 2017 Paper 1, Q15
Meal Deal
Choose one sandwich, one drink and one snack
Meal Deal
Choose one sandwich, one drink and one snack
There are
8 different sandwiches
4 different drinks
and
5 different snacks.
There are
8 different sandwiches
4 different drinks
and
5 different snacks.
1 (a)
How many different Meal Deal combinations are there?
1 (a)
How many different Meal Deal combinations are there?
[2 marks]
[2 marks]
Answer
Answer
1 (b)
Three of the sandwiches have cheese in them.
Two of the drinks are fizzy.
Eva picks a Meal Deal at random.
Work out the probability that the sandwich has cheese in it
and the drink is fizzy.
Give your answer as a fraction.
1 (b)
Three of the sandwiches have cheese in them.
Two of the drinks are fizzy.
Eva picks a Meal Deal at random.
Work out the probability that the sandwich has cheese in it
and the drink is fizzy.
Give your answer as a fraction.
[2 marks]
[2 marks]
Answer
Answer

13. AQA Higher: June 2018 Paper 3, Q17 AQA Higher: June 2018 Paper 3, Q17
Here are two methods to make a 4-digit code.
Codes can have repeated digits. 1
Here are two methods to make a 4-digit code.
Codes can have repeated digits.
Method A
For the first two digits use an odd number between 30 and 100
For the last two digits use a multiple of 11
Method A
For the first two digits use an odd number between 30 and 100
For the last two digits use a multiple of 11
Method B
Use four digits in the order even odd even odd
Do not use the digit zero
Method B
Use four digits in the order even odd even odd
Do not use the digit zero
Which method gives the greater number of possible codes?
You must show your working.
Which method gives the greater number of possible codes?
You must show your working.
[3 marks]
[3 marks]
Answer
Answer

15. AQA Higher: June 2017 Paper 2, Q5
A code has 4 digits.
Each digit is a number from 0 to 9
Digits may be repeated.
The code starts 9 8 5 9 8 5
[1 mark]
1 (a)
Alice chooses a number at random for the last digit.
Write down the probability that she chooses the correct number.
Answer
1 (b)
[1 mark]
Trevor knows the last digit is odd but not 1 or 9.
He chooses a different odd number at random.
What is the probability that he chooses the correct number?.
Answer

16. AQA Higher: June 2017 Paper 3, Q9
There are 660 boys and 840 girls in a school.
The probability that a boy chosen at random studies Drama is 2 5
The probability that a girl chosen at random studies Drama is 3 7
1 (a)
Work out the number of students in the school who study Drama.
[3 marks]
Answer
1 (b)
Work out the probability that a student chosen at random
from the whole school does not study Drama.
[2 marks]
Answer

17. Choose one sandwich, one drink and one snack
AQA Higher: November 2017 Paper 1, Q15 1
Meal Deal
Choose one sandwich, one drink and one snack
There are
8 different sandwiches
4 different drinks
and
5 different snacks.
1 (a)
How many different Meal Deal combinations are there?
[2 marks]
Answer
1 (b)
Three of the sandwiches have cheese in them.
Two of the drinks are fizzy.
Eva picks a Meal Deal at random.
Work out the probability that the sandwich has cheese in it
and the drink is fizzy.
Give your answer as a fraction.
[2 marks]
Answer

18. AQA Higher: June 2018 Paper 3, Q27
A bag contains 30 discs.
10 are red and 20 are blue.
One disc is taken out at random and replaced by
two of the other colour.
Another disc is then taken out at random and replaced by
Another disc is then taken out at random.
Work out the probability that all three discs taken out are red.
[3 marks]
Answer

19. Choose one sandwich, one drink and one snack
AQA Higher: November 2017 Paper 1, Q15 1
Meal Deal
Choose one sandwich, one drink and one snack
There are
8 different sandwiches
4 different drinks
and
5 different snacks.
1 (a)
How many different Meal Deal combinations are there?
[2 marks]
Answer
1 (b)
Three of the sandwiches have cheese in them.
Two of the drinks are fizzy.
Eva picks a Meal Deal at random.
Work out the probability that the sandwich has cheese in it
and the drink is fizzy.
Give your answer as a fraction.
[2 marks]
Answer

20. AQA Higher: June 2018 Paper 3, Q17
Here are two methods to make a 4-digit code.
Codes can have repeated digits.
Method A
For the first two digits use an odd number between 30 and 100
For the last two digits use a multiple of 11
Method B
Use four digits in the order even odd even odd
Do not use the digit zero
Which method gives the greater number of possible codes?
You must show your working.
[3 marks]
Answer

21. AQA Higher: June 2017 Paper 2, Q5
A code has 4 digits.
Each digit is a number from 0 to 9
Digits may be repeated.
The code starts 9 8 5 9 8 5
[1 mark]
1 (a)
Alice chooses a number at random for the last digit.
Write down the probability that she chooses the correct number.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 = 10
1 10
Answer
1 (b)
[1 mark]
Trevor knows the last digit is odd but not 1 or 9.
He chooses a different odd number at random.
What is the probability that he chooses the correct number?.
1, 3, 5, 7, 9 × ×
1 3
Answer

22. Boys: 660 × 2 5 = 264 Girls: 840 × 3 7 = 360 Total = 240 + 360 = 624
AQA Higher: June 2017 Paper 3, Q9 1
There are 660 boys and 840 girls in a school.
The probability that a boy chosen at random studies Drama is 2 5
The probability that a girl chosen at random studies Drama is 3 7
1 (a)
Work out the number of students in the school who study Drama.
Boys: 660 × = 264
[3 marks]
Girls: 840 × = 360
Total = = 624
Answer
1 (b)
Work out the probability that a student chosen at random
from the whole school does not study Drama.
[2 marks]
Total students = = 1500
NOT drama = 1500 – 624 = 876
73 125 OR
Answer

23. Choose one sandwich, one drink and one snack
AQA Higher: November 2017 Paper 1, Q15 1
Meal Deal
Choose one sandwich, one drink and one snack
There are
8 different sandwiches
4 different drinks
and
5 different snacks.
1 (a)
How many different Meal Deal combinations are there?
[2 marks]
8 × 4 × 5 = 8 × 20 = 160
Answer
1 (b)
Three of the sandwiches have cheese in them.
Two of the drinks are fizzy.
Eva picks a Meal Deal at random.
Work out the probability that the sandwich has cheese in it
and the drink is fizzy.
Give your answer as a fraction.
[2 marks]
Cheese: 3 8
3 8 × 2 4 = 6 32 = 3 16
Fizzy: 2 4
Answer

24. 1st Red 9 red 20 + 2 blue 31 total 1 3 2nd Red 8 red 22 + 2 blue
AQA Higher: June 2018 Paper 3, Q27 1
A bag contains 30 discs.
10 are red and 20 are blue.
One disc is taken out at random and replaced by
two of the other colour.
Another disc is then taken out at random and replaced by
Another disc is then taken out at random.
Work out the probability that all three discs taken out are red.
1st Red
9 red
blue
31 total
[3 marks]
1 3
2nd Red
8 red
blue
32 total
9 31
3rd Red
1 × 9 × 8 3 × 31 × 32 =
8 32
0.0242
4dp
Answer

25. First two digits: odd numbers between 30 and 100
AQA Higher: June 2018 Paper 3, Q17 1
Here are two methods to make a 4-digit code.
Codes can have repeated digits.
XX XX
Method A
For the first two digits use an odd number between 30 and 100
For the last two digits use a multiple of 11
Method B
Use four digits in the order even odd even odd
Do not use the digit zero
Which method gives the greater number of possible codes?
You must show your working.
Method A
[3 marks]
First two digits: odd numbers between 30 and 100
= (100 − 30) ÷ 2 = 35 options
Second two digits: 11, 22, 33 etc = 9 options
Total options = 35 × 9 = 315
Method B
Even digits = 2, 4, 6, 8 = 4 options
Odd digits = 1, 3, 5, 7, 9 = 5 options
4 × 5 × 4 × 5 = 400
Method B
Answer

26. Choose one sandwich, one drink and one snack
AQA Higher: November 2017 Paper 1, Q15 1
Meal Deal
Choose one sandwich, one drink and one snack
There are
8 different sandwiches
4 different drinks
and
5 different snacks.
1 (a)
How many different Meal Deal combinations are there?
[2 marks]
8 × 4 × 5 = 8 × 20 = 160
Answer
1 (b)
Three of the sandwiches have cheese in them.
Two of the drinks are fizzy.
Eva picks a Meal Deal at random.
Work out the probability that the sandwich has cheese in it
and the drink is fizzy.
Give your answer as a fraction.
[2 marks]
Cheese: 3 8
3 8 × 2 4 = 6 32 = 3 16
Fizzy: 2 4
Answer

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