Foundation November 2021 Paper 3 Q17

OCRFoundationCurrent spec4 marksBasic Probability

17 Ling throws a six-sided dice 300 times.
The table shows the frequencies of their results.

(a) Complete the table to show the relative frequencies.

[2]

(b) Ling thinks that the dice may be biased.

(i) Explain why evidence from the table could support their opinion. [1]

(ii) Explain why the dice may, in fact, not be biased. [1]

Answer	Marks	Part marks and guidance
0.14, 0.09, (0.19), 0.2[0], 0.13, 0.25	2	B1 for three or four correct relative frequencies in the correct place	Accept fractions

Mark scheme (b)

Answer	Marks	Part marks and guidance
(i) [Unbiased dice] would have each [rf =] 0.16–0.17 or [Unbiased dice] would have each [f =] 50 or comment about very unequal [relative] frequencies and implied comparison	1		Accept “about 0.16” Accept “about 50” Not enough to say one number was rolled the most. Must say 6 [and 4] or some numbers are much higher or 2 or 5 or some numbers are much lower
(ii) need larger sample oe	1

Exemplar responses for Q17b(i)

Response		Mark
The frequency of 2 is much lower than for the rest of the numbers	OK as MUCH lower (and for 2)	1
6 has a much larger number than the all the other numbers	Allow for “much” [and mention of the other numbers]	1
Frequency of rolling the numbers are very high compared to others such as 27 – 75 big difference	BOD 27 and 75 implying 2 and 6 and a BIG difference	1
It lands on a certain number most of the time	Does not say which number and most is not enough	0
It has a higher chance of landing on the same number	Does not say much higher or which number	0
It may be biased as the frequency of a number changes all the time	Only different not very different	0
Because 6 was rolled 75 times	Does not compare to other numbers or mention expected frequency	0
One number was rolled the most	Not enough as most could just be one more	0
6 seemed to be landed on more than any other	Does not mention MUCH oe	0
Dice landed on 6, 75 times	Doesn’t compare using MUCH oe	0
The number 6 was most frequent and 2 was least frequent	Doesn’t mention MUCH oe	0
It’s bound to land on every number almost the same number of times	And so… nothing said to answer the question	0
Number is considerably higher than all the others	Doesn’t say “Some numbers” or identify 6	0
Some numbers have a higher frequency that others	Doesn’t mention MUCH oe	0

Exemplar responses for Q17b(ii)

Response		Mark
It has not been thrown enough times	Indicates needs more trials	1
It depends on how you throw the dice		0
The larger/smaller numbers may just be anomalies	Does not indicate needs more trials	0
It could land on any number at any time, there is no specific way to get a certain number	Does not indicate needs more trials	0