Photo AI
Ling throws a six-sided dice 300 times - OCR - GCSE Maths - Question 17 - 2021 - Paper 3
Question 17
Ling throws a six-sided dice 300 times. The table shows the frequencies of their results. Number on dice | 1 | 2 | 3 | 4 | 5 | 6 | Frequency | 42 | 27 | 57 | 60 | 3... show full transcript
Worked Solution & Example Answer:Ling throws a six-sided dice 300 times - OCR - GCSE Maths - Question 17 - 2021 - Paper 3
Step 1
Complete the table to show the relative frequencies.
Answer
To find the relative frequency for each outcome on the dice, we use the formula:
Since Ling threw the dice 300 times, we can compute relative frequencies:
- For number 1:
- For number 2:
- For number 3:
- For number 4:
- For number 5:
- For number 6:
Thus, the completed relative frequency table is:
| Number on dice | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 42 | 27 | 57 | 60 | 39 | 75 |
| Relative freq | 0.14 | 0.09 | 0.19 | 0.20 | 0.13 | 0.25 |
Step 2
Explain why evidence from the table could support their opinion.
Answer
The frequencies of the numbers rolled do not appear to be uniform. For example, while the outcome for number 6 has the highest frequency (75 times), the outcome for number 2 has the lowest frequency (27 times). If the dice were fair, one would expect the frequencies to be more evenly distributed. This significant discrepancy could lead to the conclusion that the dice may be biased.
Step 3
Explain why the dice may, in fact, not be biased.
Answer
The variation in frequencies may be due to random chance. With a finite number of rolls (300), it is possible to see uneven distributions simply due to luck. Additionally, conducting further trials with a larger number of rolls could lead to different frequencies that may appear more balanced. Therefore, without additional evidence or testing, we cannot definitively conclude that the dice are biased.