Higher November 2017 Paper 6 Q11

OCRHigherCurrent spec5 marksTree Diagrams

11 Reuben is playing a matching game with these cards.

Nine cards in a row: four cards show a circle and five cards show a square

He turns the cards over and shuffles them.
Reuben takes a card and keeps it. He then takes a second card.
If the cards are different, he wins the game.

(a) Complete this tree diagram to show the probabilities for each card picked in the game.

Tree diagram: first card Circle with probability 4/9 or Square (blank); second card branches Circle or Square from each, all blank

[2]

(b) What is the probability that Reuben wins the game? [3]

Answer	Marks	Part marks and guidance
	2	B1 for \(\dfrac{5}{9}\) and at least one fraction with denominator 8 for second card

Mark scheme (b)

Answer	Marks	Part marks and guidance
\(\dfrac{5}{9}\) oe	3	M2FT for \(\left(\dfrac{4}{9} \times \dfrac{5}{8}\right) + \left(\dfrac{5}{9} \times \dfrac{4}{8}\right)\) oe OR M1FT for \(\left(\dfrac{4}{9} \times \dfrac{5}{8}\right)\) or \(\left(\dfrac{5}{9} \times \dfrac{4}{8}\right)\) oe soi by \(\dfrac{20}{72}\) oe	FT their probabilities from (a)