Handling Data 4
6 marks · HardA six-sided die is rolled 48 times. The frequencies for each face are shown below:
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 10 | 9 | 12 | 6 | 7 | 4 |
(a) Calculate the experimental probability of rolling a 5.
(b) If the die is fair, calculate the expected frequency of rolling a 5 in 48 throws.
(c) Based on the table, discuss whether the die is likely to be fair, giving a reason for your answer.
Calculate the experimental probability of rolling a 5.
If the die is fair, calculate the expected frequency of rolling a 5 in 48 throws.
Based on the frequencies in the table, discuss whether the die is likely to be fair, giving a reason for your answer.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) 0.146
(b) 8
(c) No, the frequencies differ significantly from what would be expected if the die were fair. Several numbers appear much more or less than expected; for example, '6' appeared only 4 times instead of around 8.
Common mistakes: dividing by wrong total; using theoretical probability for part a; misreading frequencies
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Marking points
M1 (a) · 1 mark · Correct method: frequency of 5 divided by total throws.
A1 (a) · 1 mark · Correct answer for experimental probability (to 3 sf). (follow-through)
M2 (b) · 1 mark · Correct method: total throws × 1/6.
A2 (b) · 1 mark · Correct value for expected frequency (rounded). (follow-through)
M3 (c) · 1 mark · Compares observed frequencies to expected and makes judgement systematically.
A3 (c) · 1 mark · States at least one concrete example, and conclusion (e.g., number 6 very low, not fair). (follow-through)
Worked solution
(a) Experimental probability for 5 = 7 / 48 ≈ 0.146.
(b) Expected frequency = 48 × 1/6 = 8.
(c) Most faces appear about 8 times if the die is fair. Here, 6 appears only 4 times, 3 appears 12 times, and 5 appears 7 times. The large difference, especially face '6' being much less than expected, suggests the die may not be fair.