Higher June 2023 Paper 2 Q10
10 A biased dice is thrown 60 times.
The table shows information about the number that the dice lands on each time.
| Number on dice | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 12 | 7 | 8 | 9 | 9 | 15 |
Gethin throws the dice twice.
(a) Work out an estimate for the probability that the dice will land on 6 both times. (3)
Sally is going to throw the same dice \(n\) times and record the number it lands on each time.
She will use her results to work out a more reliable estimate for the probability in part (a).
(b) What can you say about the value of \(n\)? (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{225}{3600}\) | P1 | for process to use relative frequency for landing on a 6, eg \(\dfrac{15}{60}\) oe |
| P1 | for \(\dfrac{15}{60} \times \dfrac{15}{60}\) oe, eg \(\dfrac{1}{4} \times \dfrac{1}{4}\) | |
| A1 | for \(\dfrac{225}{3600}\) oe, eg \(\dfrac{1}{16}\) |
Additional guidance
Accept any equivalent fraction, decimal form 0.06(25) or 0.062 or 0.063, percentage form 6(.25)% or 6.2% or 6.3%
Ignore subsequent attempts to write the correct answer in a different form.
| Answer | Mark | Mark scheme |
|---|---|---|
| Explanation | C1 | for a correct explanation Acceptable examples \(n\) must be greater than 60 She must do it more times than in (a) \(n\) must be bigger, eg 100 Not acceptable examples If you increase the number of results, you increase the accuracy \(n\) must be bigger \(n\) is an integer \(n\) is 100 |