Higher June 2019 Paper 6 Q12
12 Antonio rolls two fair six-sided dice and calculates the difference between the scores.
For example, if the two scores are 2 and 5 or 5 and 2 then the difference is 3.
(a) Complete the sample space diagram to show the possible outcomes from Antonio’s dice.
| difference | Dice 2 | ||||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | ||
| Dice 1 | 1 | 0 | |||||
| 2 | 3 | ||||||
| 3 | 1 | ||||||
| 4 | |||||||
| 5 | 3 | ||||||
| 6 | |||||||
[2]
(b) Antonio rolls the two dice three times.
Calculate the probability that he gets a difference of 1 on all three rolls.
Give your answer as a fraction in its lowest terms. [4]
| Answer | Marks | Part marks and guidance | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | B1 for at least 10 correct entries | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\dfrac{125}{5832}\) | 4 | B3 for \(\dfrac{1000}{46656}\) oe isw wrong cancelling or for 0.0214(33…) oe as final answer OR B1FT for \(\dfrac{10}{36}\) oe and M1 for their \(\dfrac{10}{36}\) × their \(\dfrac{10}{36}\) × their \(\dfrac{10}{36}\) | FT from their completed table in part (a) \(\dfrac{10}{36} = \dfrac{5}{18}\) = 0.2777… to 0.278 Common mistake: B1 M0 for \(3 \times \dfrac{10}{36}\) |