Basic Probability: Eduqas GCSE Foundation June 2022 Paper 2 Q5

Foundation June 2022 Paper 2 Q5

5. Roman has the nine cards shown below.

You must only use the numbers on these cards.
You must show all your working.

(a)

(i) Calculate the sum of the two prime numbers. [2]

(ii) Calculate the product of the two square numbers. [2]

(iii) Find the number which is both a factor of 72 and a multiple of 8. [2]

(b)

Roman picks one of his nine cards at random.
He says,

“I have a \(\frac{2}{9}\) chance of picking a card with a cube number on it.”

Is Roman’s statement correct?

Yes ☐ No ☐

Show how you decide. [1]

Mark scheme (a)

Scheme	Marks	Comments
(i) (13 + 17 =) 30	B2	Award B1 for either of: Identifying 13 AND 17 and no others A correct evaluation of (13 + x) or (17 + y) where x and y are numbers from the cards.
(ii) (9 × 36 =) 324	B2	Award B1 for either of: Identifying 9 AND 36 and no others A correct evaluation of (9 × a) or (36 × b) where a and b are numbers from the cards
(iii) 24	B2	B1 for an answer of 9, 32 or 36 (a number satisfying one of the conditions) Allow B1 for 24 with one extra providing it is 9, 32 or 36

Mark scheme (b)

Scheme	Marks	Comments
Unambiguously stating or implying ‘No’ with a reason, e.g. ‘the chance is 1/9’, ‘one cube number not two’, ‘27 is the only cube number so 1/9 chance’	E1	Allow ‘No’ and ‘27 is the only cube number’ ‘only one cube number’ ‘there are not two cube numbers’ Do not allow ‘3 x 3 x 3 = 27’ ’27 = cube number’
	(7)