4MA0 Higher June 2017 Paper 3R Q11

EdexcelHigherOld spec7 marksTree Diagrams

11 There are 9 red counters and 11 blue counters in a bag.
There are no other counters in the bag.

Emeka takes at random a counter from the bag and writes down the colour of the counter.
He puts the counter back in the bag.
Natasha takes at random a counter from the bag and writes down the colour of the counter.

(a) Complete the probability tree diagram. (2)

Probability tree diagram: Emeka branches red with probability 9/20 and blue with a blank probability; Natasha branches not drawn

(b) Work out the probability that Emeka takes a red counter from the bag and Natasha takes a blue counter from the bag. (2)

Mark scheme (a)

Scheme	Marks
Complete correct binary structure for selection of two counters OR At least one additional red branch labelled \(\dfrac{9}{20}\) and at least two blue branches labelled \(\dfrac{11}{20}\)	M1
Correct probability tree diagram	A1
	(2)

Mark scheme (b)

Scheme	Marks
\(\dfrac{9}{20} \times \dfrac{11}{20}\)	M1
\(\dfrac{99}{400}\)	A1
	(2)

Notes

M1: for \(\text{‘}\dfrac{9}{20}\text{’} \times \text{‘}\dfrac{11}{20}\text{’}\)

A1: (ft diagram) for \(\dfrac{99}{400}\) or 0.2475 or 24.75%

Mark scheme (c)

Scheme	Marks
\(\text{‘}\dfrac{9}{20}\text{’} \times \text{‘}\dfrac{9}{20}\text{’}\) or \(\text{‘}\dfrac{11}{20}\text{’} \times \text{‘}\dfrac{11}{20}\text{’}\)	M1
\(\text{‘}\dfrac{9}{20}\text{’} \times \text{‘}\dfrac{9}{20}\text{’} + \text{‘}\dfrac{11}{20}\text{’} \times \text{‘}\dfrac{11}{20}\text{’}\)	M1
\(\dfrac{202}{400}\)	A1
	(3)
	(7 marks)

Notes

M1: for one correct product
ft from diagram

M1: for the complete method
ft from diagram

A1: \(\dfrac{202}{400}\) oe or 0.505 or 50.5%

Alternative method

M1 for \(2 \times \text{‘}\dfrac{9}{20}\text{’} \times \text{‘}\dfrac{11}{20}\text{’}\) oe (ft from (a))
M1 for \(1 - 2 \times \text{‘}\dfrac{9}{20}\text{’} \times \text{‘}\dfrac{11}{20}\text{’}\)