Higher June 2023 Paper 6 Q3

OCRHigherCurrent spec6 marksBasic Probability

3 A bag contains 150 counters.
The counters are either red or yellow.

(a) Riley picks a counter from the bag, records its colour, and replaces it.
They do this nine times.

Here are Riley’s results.

Tally chart: Red, a tally of 5; Yellow, a tally of 4

Use Riley’s results to work out how many red counters are likely to be in the bag. [3]

(b) Ling uses the same bag of counters and picks the counters in the same way.

Here are Ling’s results.

Tally chart: Red, a tally of 12; Yellow, a tally of 8

Use Ling’s results to estimate the probability of choosing a red counter from the bag.
Give your answer as a fraction in its simplest form. [2]

(c) Explain why Ling’s results are likely to give a better estimate of the probability of choosing a red counter from the bag than Riley’s results. [1]

Mark scheme (a)

Answer	Marks	Part marks and guidance
83 or 84	3	M2 for 150 × \(\frac{5}{9}\) oe implied by answer 83.3… or M1 for \(\frac{5}{9}\) or for \(\frac{150}{9}\)	Non calculator methods must be fully correct, see appendix, and would lead to 83.3 May be implied by 0.55 to 0.56 or 55% to 56% May be implied by 16.6 to 16.7

Appendix

Non Calculator methods for percentages.

Labels only
This is when labels such as 10% = are used. If only labels are used the final answer scores full marks if it is correct.
Condone a numerical slip if the answer is correct.
If there is an error in the values and so the final answer is incorrect this cannot score method marks
e.g. Find 65% of 60

Method scoring M1A1
10% = 6
5% = 3
50% = 30
65% = 39 ✓ M1A1

10% = 6
5% = 4 ✗ condone this slip as answer correct
50% = 30
65% = 39 ✓ M1A1

Method scoring M0A0
10% = 6
5% = 4 ✗ M0 Do not condone this slip as answer incorrect
50% = 30
65% = 40 ✗

Build up method
This is where the candidate finds the percentages to build up to the required value but shows the operations used.
e.g. Find 65% of 60
10% = 60 ÷ 10 = \(x\)
5% = \(x\) ÷ 2 = \(y\)
50% = \(x\) × 5 = \(z\)
65% = \(x + z + y\)
Because the operations have been shown and they are correct, if there is an error in one of \(x\), \(y\) or \(z\), method marks can still be earned

Answer	Marks	Part marks and guidance
\(\frac{3}{5}\)	2	B1 for \(\frac{12}{20}\) oe	For B1 accept 0.6 or 60% or \(\frac{12}{20}\) × 150

Mark scheme (c)

Answer	Marks	Part marks and guidance
[Ling has] more results [than Riley] oe	1		See appendix Accept he/they/she as reference to Ling May be inverse: [Riley has] fewer results [than Ling] oe Do not accept comments about more/less in the bag

Appendix: Question 3c

Response	Comment	Mark
Ling chose more counters		1
There is more counters	BOD as does not say “in the bag” and could mean “in the sample”	1 bod
Lin picked more times		1
Ling took more samples		1
Ling took a larger sample	Could mention numbers such as “more than 9”	1
She has more in the tally	BOD	1
Ling did it 20 times and Riley did it 9 times	BOD a comparison (would be better if “only” included)	1
There are more counters in the bag	This is untrue	0
Ling did it multiple times	Not a comparison (we have to do the comparing)	0
Ling did it 20 times	Not a comparison (we have to do the comparing)	0