Multiple Events: WJEC GCSE Intermediate November 2023 Unit 2 Q15

Intermediate November 2023 Unit 2 Q15

WJECIntermediateCurrent spec4 marksMultiple Events

15. Vera has two fair spinners.
Each spinner is divided into quarters.
One spinner shows the values 1, 2, 3 and 4.
The other spinner shows the values 6, 7, 8 and 9.

Two spinners divided into quarters: the first shows 1, 2, 3, 4 with the arrow pointing at 1; the second shows 6, 7, 8, 9 with the arrow pointing at 7

Vera spins the two spinners. She then multiplies the two values together to form a product.
For example, the diagram above forms the product \(1 \times 7 = 7\).

Consider the ways in which all the possible products can be formed.
Calculate the probability that the spinners will form a product that is a factor of 36.
You must show all your working to justify your answer. [4]

Mark scheme

Scheme	Marks	Comments
Identifying or implying that there are 16 possible correct combinations (e.g 2 × 6) or products (e.g.12)	B1	Award B1 for simply stating 16 (4 × 4 =)16 completed sample space (need not be correct) sight of \(\tfrac{1}{4} \times \tfrac{1}{4}\) sight of 16 in a denominator.
Identifies all possible combinations (e.g 2 × 6) or products (e.g 12) that are a factor of 36 1 × 6 = 6, 1 × 9 = 9, 2 × 6 = 12 2 × 9 = 18, 3 × 6 = 18, 4 × 9 = 36	B2	FT ‘their 16 possible correct products’. If products not used (e.g 2 + 6 = 8), do not award B2 or B1. Award B2 for clearly identifying one of the following: the 6 (and no more) combinations 1 × 6, 2 × 9, etc that form factors of 36 that can be achieved by the two spinners the 6 (and no more) products of factors of 36 that can be achieved by the two spinners: 6, 9, 12, 18, 18, 36 sight of \(6 \times \tfrac{1}{4} \times \tfrac{1}{4}\) or equivalent. Award B1 for clearly identifying one of the following: at least 4 combinations that are factors of 36 at least 4 products of factors of 36 that can be achieved by the two spinners: 6, 9, 12, 18, 36 all of the factors of 36 (1,2,3,4,6,9,12,18,36).
(Probability factor of 36 =) \(\dfrac{6}{16}\) or equivalent. ISW	B1	FT ‘their list’ only if at least 12 combinations or products given with at least two factors of 36 that can be achieved by the two spinners clearly identified. Penalise, −1, any incorrect notation e.g. ‘6 out of 16’. Unsupported \(\dfrac{6}{16}\) or \(\dfrac{3}{8}\) or equivalent gains B1 B2 B1.

Scheme

Marks

Comments

Identifying or implying that there are 16 possible correct combinations (e.g 2 × 6) or products (e.g.12)

Award B1 for

simply stating 16
(4 × 4 =)16
completed sample space (need not be correct)
sight of \(\tfrac{1}{4} \times \tfrac{1}{4}\)
sight of 16 in a denominator.

Identifies all possible combinations (e.g 2 × 6) or products (e.g 12) that are a factor of 36
1 × 6 = 6, 1 × 9 = 9, 2 × 6 = 12
2 × 9 = 18, 3 × 6 = 18, 4 × 9 = 36

FT ‘their 16 possible correct products’.
If products not used (e.g 2 + 6 = 8), do not award B2 or B1.

Award B2 for clearly identifying one of the following:

the 6 (and no more) combinations
1 × 6, 2 × 9, etc that form factors of 36 that can be achieved by the two spinners
the 6 (and no more) products of factors of 36 that can be achieved by the two spinners: 6, 9, 12, 18, 18, 36
sight of \(6 \times \tfrac{1}{4} \times \tfrac{1}{4}\) or equivalent.

Award B1 for clearly identifying one of the following:

at least 4 combinations that are factors of 36
at least 4 products of factors of 36 that can be achieved by the two spinners:
6, 9, 12, 18, 36
all of the factors of 36 (1,2,3,4,6,9,12,18,36).

(Probability factor of 36 =) \(\dfrac{6}{16}\) or equivalent. ISW

FT ‘their list’ only if at least 12 combinations or products given with at least two factors of 36 that can be achieved by the two spinners clearly identified.

Penalise, −1, any incorrect notation e.g. ‘6 out of 16’.

Unsupported \(\dfrac{6}{16}\) or \(\dfrac{3}{8}\) or equivalent gains B1 B2 B1.