1 of 66

91267 – Worked Solutions - 2025

2 of 66

QUESTION TWO

3 of 66

2.12 (AS 91267) – 2025 Answers

Quite often, there are different ways to solve a Mathematics problem.

These solutions/strategies show one possible way to solve them.

​

Question 2 (a) i

​

Question 2 (a) ii

​

Question 2 (b) i

​

Question 2 (b) ii

​

Question 2 (b) iii

4 of 66

Question 2(a)

  •  

5 of 66

Question 2(a)

  •  

6 of 66

Question 2(a)

  •  

7 of 66

Question 2(a)

  •  

8 of 66

Question 2(a)

  •  

9 of 66

Question 2(a)

  •  

10 of 66

Question 2(a)

  •  

11 of 66

Question 2(a)

  •  

12 of 66

Question 2(a)

  •  

 

13 of 66

Question 2(a)

  •  

14 of 66

Question 2(a)

  •  

 

15 of 66

Question 2(a)

  •  

 

16 of 66

Question 2(a)

  •  

 

17 of 66

Question 2(a)

  •  

 

18 of 66

Question 2(a)

  •  

 

19 of 66

Question 2(a)

  •  

20 of 66

Question 2(a) i

(i) What is the probability that a customer chooses pancakes and fruit for breakfast?

21 of 66

Question 2(a) i

(i) What is the probability that a customer chooses pancakes and fruit for breakfast?

22 of 66

Question 2(a) i

(i) What is the probability that a customer chooses pancakes and fruit for breakfast?

23 of 66

Question 2(a) i

(i) What is the probability that a customer chooses pancakes and fruit for breakfast?

24 of 66

Question 2(a) i

(i) What is the probability that a customer chooses pancakes and fruit for breakfast?

 

25 of 66

Question 2(a) ii

(ii) For a randomly selected group of 250 customers, how many customers would you expect to choose yoghurt?

26 of 66

Question 2(a) ii

(ii) For a randomly selected group of 250 customers, how many customers would you expect to choose yoghurt?

27 of 66

Question 2(a) ii

(ii) For a randomly selected group of 250 customers, how many customers would you expect to choose yoghurt?

 

28 of 66

Question 2(a) ii

(ii) For a randomly selected group of 250 customers, how many customers would you expect to choose yoghurt?

 

29 of 66

Question 2(a) ii

(ii) For a randomly selected group of 250 customers, how many customers would you expect to choose yoghurt?

 

30 of 66

Question 2(a) ii

(ii) For a randomly selected group of 250 customers, how many customers would you expect to choose yoghurt?

 

31 of 66

Question 2(a) ii

(ii) For a randomly selected group of 250 customers, how many customers would you expect to choose yoghurt?

 

 

32 of 66

Question 2(a) ii

(ii) For a randomly selected group of 250 customers, how many customers would you expect to choose yoghurt?

 

 

33 of 66

Question 2(b)

  •  

34 of 66

Question 2(b)

  •  

35 of 66

Question 2(b)

  •  

 

36 of 66

Question 2(b)

  •  

 

37 of 66

Question 2(b)

  •  

 

38 of 66

Question 2(b)

  •  

 

39 of 66

Question 2(b)

  •  

 

40 of 66

Question 2(b)

  •  

 

41 of 66

Question 2(b)

  •  

42 of 66

Question 2(b) i

(i) What proportion of the cafe’s customers do not win?

43 of 66

Question 2(b) i

(i) What proportion of the cafe’s customers do not win?

44 of 66

Question 2(b) i

(i) What proportion of the cafe’s customers do not win?

45 of 66

Question 2(b) i

(i) What proportion of the cafe’s customers do not win?

 

46 of 66

Question 2(b) i

(i) What proportion of the cafe’s customers do not win?

 

47 of 66

Question 2(b) i

(i) What proportion of the cafe’s customers do not win?

 

48 of 66

Question 2(b) ii

(ii) What is the probability that a customer who spends over $100 next month wins a free coffee?

49 of 66

Question 2(b) ii

(ii) What is the probability that a customer who spends over $100 next month wins a free coffee?

50 of 66

Question 2(b) ii

(ii) What is the probability that a customer who spends over $100 next month wins a free coffee?

51 of 66

Question 2(b) ii

(ii) What is the probability that a customer who spends over $100 next month wins a free coffee?

 

52 of 66

Question 2(b) ii

(ii) What is the probability that a customer who spends over $100 next month wins a free coffee?

 

53 of 66

Question 2(b) ii

(ii) What is the probability that a customer who spends over $100 next month wins a free coffee?

 

54 of 66

Question 2(b) ii

(ii) What is the probability that a customer who spends over $100 next month wins a free coffee?

 

55 of 66

Question 2(b) ii

(ii) What is the probability that a customer who spends over $100 next month wins a free coffee?

 

56 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

57 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

58 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

59 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

60 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

 

61 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

 

62 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

 

63 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

 

64 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

 

65 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

 

0.75

0.25

66 of 66

Question 2(b) iii

(iii) Those customers who spent over $100, but did not win a free coffee or $20 voucher, can now win one of two consolation prizes, a badge or a sticker. The probability of a random customer winning a badge is 0.21.

What is the probability of a customer winning a sticker, given they have won a consolation prize?

 

0.75

0.25

The probability of a customer winning a sticker, given they have won a consolation prize = 0.25.