Photo AI
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 frequencies, divide each frequency by the total number of throws (300).
For example:
-
For number on dice 1: [ \text{Relative Frequency} = \frac{42}{300} = 0.14 ]
-
For number on dice 2: [ \text{Relative Frequency} = \frac{27}{300} = 0.09 ]
-
For number on dice 3:
[ \text{Relative Frequency} = \frac{57}{300} = 0.19 ] -
For number on dice 4:
[ \text{Relative Frequency} = \frac{60}{300} = 0.20 ] -
For number on dice 5:
[ \text{Relative Frequency} = \frac{39}{300} = 0.13 ] -
For number on dice 6:
[ \text{Relative Frequency} = \frac{75}{300} = 0.25 ]
The completed table is:
| 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
The frequencies of the results show that not all outcomes are equally likely. For example, the frequency for the number 6 (75) is significantly higher than that of the number 2 (27). Such discrepancies from expected uniform distribution (where each number should ideally occur approximately 50 times in 300 throws) may suggest that the dice could be biased.
Step 3
Explain why the dice may, in fact, not be biased.
Answer
The observed frequencies could be a result of random variation. With a relatively small number of throws (300), it's possible to see fluctuations in the results due to chance. As more throws are conducted, the relative frequencies may begin to converge towards the expected uniform distribution, indicating that the dice may not be biased.