4MA0 Higher January 2017 Paper 4 Q14

EdexcelHigherOld spec6 marksTree Diagrams

14 There are 52 cards in a pack.
12 cards are picture cards.
40 cards are number cards.

Melina takes at random a card from the pack.
She keeps the card and then takes at random a second card from the remainder of the pack.

(a) Complete the probability tree diagram. (3)

(b) Work out the probability that the two cards Melina takes are both picture cards or both number cards. (3)

Mark scheme (a)

Scheme	Marks
\(\dfrac{12}{52}, \dfrac{40}{52}, \dfrac{11}{51}, \dfrac{40}{51}, \dfrac{12}{51}, \dfrac{39}{51}\)	B3
	(3)

B3: B1 for each pair.

Accept equivalent fractions

\(\dfrac{12}{52} = \dfrac{3}{13}, \dfrac{40}{52} = \dfrac{10}{13}, \dfrac{12}{51} = \dfrac{4}{17}, \dfrac{39}{51} = \dfrac{13}{17}\)

Accept equivalent decimals correct to at least 2dp (0.23, 0.77, 0.22, 0.78, 0.24, 0.76)

Mark scheme (b)

Scheme	Marks
\(\dfrac{12}{52} \times \dfrac{11}{51}\) or \(\dfrac{132}{2652}\) or \(\dfrac{11}{221}\) or 0.049(773...) or \(\dfrac{40}{52} \times \dfrac{39}{51}\) or \(\dfrac{1560}{2652}\) or \(\dfrac{130}{221}\) or \(\dfrac{10}{17}\) or 0.588(235...)	M1
\(\dfrac{12}{52} \times \dfrac{11}{51} + \dfrac{40}{52} \times \dfrac{39}{51}\) or \(\dfrac{132}{2652} + \dfrac{1560}{2652}\) or \(\dfrac{11}{221} + \dfrac{10}{17}\) oe	M1
\(\dfrac{141}{221}\)	A1
	(3)
	(6 marks)

M1: ft their tree diagram

A1: 0.638(009…) rounded or truncated to at least 3 DP or oe

or M2 for \(1 - \left(\dfrac{12}{52} \times \dfrac{40}{51} + \dfrac{40}{52} \times \dfrac{12}{51}\right)\) (= 1 − 0.361(99…))

Scheme	Marks
\(\dfrac{12}{52} \times \dfrac{12}{52}\) or \(\dfrac{144}{2704}\) or \(\dfrac{9}{169}\) or 0.053(254...) or \(\dfrac{40}{52} \times \dfrac{40}{52}\) or \(\dfrac{1600}{2704}\) or \(\dfrac{100}{169}\) or 0.591(715...)	M1
\(\dfrac{12}{52} \times \dfrac{12}{52} + \dfrac{40}{52} \times \dfrac{40}{52}\) or \(\dfrac{144}{2704} + \dfrac{1600}{2704}\) or \(\dfrac{9}{169} + \dfrac{100}{169}\) or \(\dfrac{1744}{2704}\) or \(\dfrac{109}{169}\) or 0.644(970....) oe	M1

or M2 for \(1 - \left(\dfrac{12}{52} \times \dfrac{40}{52} + \dfrac{40}{52} \times \dfrac{12}{52}\right)\) (= 1 − 0.355(029…))