Basic Probability: Eduqas GCSE Foundation June 2022 Paper 2 Q11

Foundation June 2022 Paper 2 Q11

EduqasFoundationCurrent spec6 marksBasic Probability

11. Faheema has a sack that contains a number of identical balls of different colours.

The table below shows the probability of randomly choosing a ball that is red, green, yellow or blue.

Colour	Red	Green	Yellow	Blue
Probability	0·32	0·46	0·1	0·12

(a)

Faheema claims:

“There are other balls that are not red, green, yellow or blue in the sack.”

Explain why she is incorrect. [1]

(b)

A ball is chosen at random from the sack.

Calculate the probability that this ball is either green or yellow. [1]

(c)

Faheema uses the sack of balls for a game at her school fair.

In the game, each person pays 50p to choose a ball at random from the sack.
The ball is then returned to the sack.

The player wins a prize worth £2.95 if a blue ball is chosen.

150 people each played the game once.

How much profit would you expect Faheema to make?
You must show all your working. [4]

Mark scheme (a)

Scheme	Marks	Comments
“the probabilities sum to 1” oe	E1	Accept e.g. 0.32 + 0.46 + 0.1 + 0.12 = 1 or 32% + 46% + 10% + 12% = 100% as an explanation Allow 32 + 46 + 10 + 12 = 100% 0.32 + 0.46 + 0.10 + 0.12 = 100% ‘The probability of other colours is 0’ ‘red + green + yellow + blue = 1’ 32 + 46 + 10 + 12 = 100 (without % signs) Do not allow e.g. 0.32 + 0.46 + 0.10 + 0.12 = 100 32 + 46 + 10 + 12 = 1 ‘the numbers are equal to 1’

Scheme	Marks	Comments
0.56 oe	B1	ISW. Allow 0.56/1

Mark scheme (c)

Scheme	Marks	Comments
(Expected no. of winners = 0.12 × 150 =) 18	B1	Working can be in pence or pounds
0.5(0) × 150 – 2.95 × 18	M2	FT ‘their derived 12% of 150’ Allow M2 only if use of inconsistent units is later corrected M1 for either 0.5 × 150 or 2.95 × ‘their derived 12% of 150’
= (£) 21.9(0) or 2190 (p)	A1	FT from M2 for a correct evaluation using ‘their derived 12% of 150’ If units are given, they must be correct.
	(6)

Alternative method

Scheme	Marks	Comments
(Expected no. of winners = 0.12 × 150 =) 18	B1
(150 – 18) × 0.5(0) – 18 × (2.95 – 0.5(0))	M2	FT ‘their derived 12% of 150’ Allow M2 only if use of inconsistent units is later corrected M1 for either (150 – 18) × 0.5(0) or 18 × (2.95 – 0.5(0))
= (£) 21.9(0) or 2190 (p)	A1	FT from M2 for a correct evaluation using ‘their derived 12% of 150’ If units are given, they must be correct