Basic Probability: Eduqas GCSE Foundation November 2024 Paper 2 Q10

Foundation November 2024 Paper 2 Q10

EduqasFoundationCurrent spec5 marksBasic Probability Forming Equations

10. Zara makes necklaces by threading beads onto lengths of string.

(a)

She uses a bag of beads that contains pink, yellow, green and blue beads.
In the bag:

half of the beads are pink
there are half as many yellow beads as pink beads
there are an equal number of green beads and blue beads.

Zara selects a bead at random from the bag.

Complete the table below to show the probability of selecting each colour. [2]

Colour	Pink	Yellow	Green	Blue
Probability

(b)

Zara makes necklaces of two different lengths.
The length of string for each long necklace is \(y\) cm.
The string for each short necklace is 11 cm shorter than the string for a long necklace.

Write an expression, in terms of \(y\), for the total length of string needed to make one long necklace and two short necklaces.
Simplify your answer. [3]

Mark scheme (a)

Scheme

Marks

Comments

All probabilities correct.

Colour	Pink	Yellow	Green	Blue
Probability	0.5, \(\frac{1}{2}\) or 50%	0.25, \(\frac{1}{4}\) or 25%	0.125, \(\frac{1}{8}\) or 12.5%	0.125, \(\frac{1}{8}\) or 12.5%

Table takes precedence.

Or equivalent.

B1 for one of the following:

P(P) = 0.5 AND P(Y) = 0.25
P(G) = P(B) = \(\frac{1}{2}\)(1 - ('their P(P) + P(Y)’)) except for P(P) = P(Y) = P(G) = P(B)

Probabilities must be > 0 and < 1

Corrected by Westie's Workshop

The board's mark scheme printed “½(1 − ('their P(P) + P(Y)’)”. Changed to “½(1 − ('their P(P) + P(Y)’))” because a closing bracket was missing.

Original: see the board's mark scheme PDF (link above).

Mark scheme (b)

Scheme	Marks	Comments
3y - 22	B3	Allow e.g. 3y – 22 cm or 3y cm – 22 cm. Mark final answer. B2 for an equivalent unsimplified expression e.g. y + 2y – 22 y + 2(y – 11) y + y + y – 11 - 11 B1 for an expression for the short necklaces simplified or unsimplified e.g. 2y – 22 2(y – 11) y – 11 + y – 11 B0 for 2 × y – 11 or y – 11 × 2 If no marks, award SC1 for y + 2 × y – 11 y + y – 11 × 2
	(5)

Scheme

Marks

Comments

3y - 22

Allow e.g. 3y – 22 cm or 3y cm – 22 cm.
Mark final answer.

B2 for an equivalent unsimplified expression e.g.

y + 2y – 22
y + 2(y – 11)
y + y + y – 11 - 11

B1 for an expression for the short necklaces simplified or unsimplified e.g.

2y – 22
2(y – 11)
y – 11 + y – 11

B0 for 2 × y – 11 or y – 11 × 2

If no marks, award SC1 for

y + 2 × y – 11
y + y – 11 × 2

(5)