Intermediate November 2022 Unit 1 Q12
12. Samira has a dice. Its faces are numbered 1 to 6.
She wants to know whether her dice is biased or not.
Samira rolled this dice 300 times.
Her results are shown in the table below.
| Number shown on dice | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 65 | 40 | 52 | 10 | 23 | 110 |
(a) The relative frequency of throwing a 5 is \(\dfrac{23}{300}\).
What is the relative frequency of throwing a 2?
Give your answer as a fraction in its simplest form. [2]
What is the relative frequency of throwing a 2?
Give your answer as a fraction in its simplest form. [2]
(b) Do the results in the table suggest that Samira’s dice is biased?
Yes ☐ No ☐
Explain your decision. [1](c) This dice is thrown 2400 times.
Use Samira’s results to calculate the number of times you would expect a 6 to be thrown. [2]
Use Samira’s results to calculate the number of times you would expect a 6 to be thrown. [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{2}{15}\) | B2 | For B2, the answer must be in its simplest form. Award B1 for sight of \(\dfrac{40}{300}\) or equivalent. |
| Scheme | Marks | Comments |
|---|---|---|
| YES ticked and a valid explanation e.g. “you would expect to get (approximately) equal frequencies if it was unbiased” “you would expect (approximately) 50 of each number” “6 was thrown a lot of times” “4 was not thrown a lot of times” “the frequencies are not the same” “All the frequencies are different.” | E1 | Award E1 if Yes or No box ticked but explanation clearly explains that the dice is biased. Allow: “they are not equal” “they are not the same”. |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{110}{300}\) × 2400 or equivalent | M1 | May be shown in stages. |
| = 880 | A1 | \(\dfrac{880}{2400}\) gains M1A0. Mark final answer. |