4400 Higher June 2007 Paper 3 Q10

EdexcelHigherOld spec8 marksBasic Probability Multiple Events

10 Here are five shapes.

Five shapes: a black square, three white squares and a black circle

Four of the shapes are squares and one of the shapes is a circle.
One square is black.
Three squares are white.
The circle is black.
The five shapes are put in a bag.

(a) Jasmine takes a shape at random from the bag 150 times.
She replaces the shape each time.
Work out an estimate for the number of times she will take a white square. (3)

(b) Alec takes a shape at random from the bag and does not replace it.
Bashir then takes a shape at random from the bag.
Work out the probability that

(i) they both take a square,

(ii) they take shapes of the same colour. (5)

Mark scheme (a)

Scheme	Marks
\(150 \times \frac{3}{5}\)	B1
	M1
90	A1
	(3)

Notes

B1: for \(\frac{3}{5}\) seen

M1: for \(150 \times \frac{3}{5}\)

A1: cao Do not accept \(\dfrac{90}{150}\)

Accept decimals in parts (a) and (b)

Mark scheme (b)

Scheme	Marks
(i) \(\frac{4}{5} \times \frac{3}{4}\)	M1
\(\frac{12}{20}\) or \(\frac{3}{5}\) oe	A1
(ii) \(\frac{2}{5} \times \frac{1}{4} + \frac{3}{5} \times \frac{2}{4}\)	M1
	M1
\(\frac{8}{20}\) or \(\frac{2}{5}\) oe	A1
	(5)
	(8 marks)

Notes

M1: for \(\frac{4}{5} \times \frac{3}{4}\) seen

M1: for \(\frac{2}{5} \times \frac{1}{4}\) or \(\frac{3}{5} \times \frac{2}{4}\)
SC M1 for \(\frac{2}{5} \times \frac{2}{5}\) or \(\frac{3}{5} \times \frac{3}{5}\)

M1: (dep) for adding both above products
SC M1 (dep) for adding both above products

A1: for \(\frac{8}{20}\) or \(\frac{2}{5}\) oe

Accept decimals in parts (a) and (b)