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Ling throws a six-sided dice 300 times - OCR - GCSE Maths - Question 5 - 2021 - Paper 1
Question 5
Ling throws a six-sided dice 300 times. The table shows the frequencies of their results. Complete the table to show the relative frequencies. | Number on dice | 1... show full transcript
Worked Solution & Example Answer:Ling throws a six-sided dice 300 times - OCR - GCSE Maths - Question 5 - 2021 - Paper 1
Step 1
Complete the table to show the relative frequencies.
Answer
To find the relative frequency for each number on the dice, use the formula:
The total number of throws is 300. Thus:
- For 1:
- For 2:
- For 3:
- For 4:
- For 5:
- For 6:
Filling the table:
| Number on dice | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 42 | 27 | 57 | 60 | 39 | 75 |
| Relative frequency | 0.14 | 0.09 | 0.19 | 0.20 | 0.13 | 0.25 |
Step 2
Explain why evidence from the table could support her opinion.
Answer
Ling's perception of bias might stem from the relative frequencies observed.
If certain numbers appear significantly more or less than expected (which would generally be around 0.1667 for a fair die), it can indicate that the die may not be fair. For instance, the frequency of number 6 (0.25) is much higher than expected, while number 2 (0.09) is lower, which raises suspicion about potential bias.
Step 3
Explain why the dice may, not be biased.
Answer
While the results suggest bias, it is important to remember that observed outcomes can vary due to random chance, especially with a small number of throws. The law of large numbers states that as the number of trials increases, the experimental probabilities will converge on the theoretical probabilities. Thus, further trials might yield results closer to expected frequencies, indicating that the observed results could be part of normal random variation.