Higher June 2022 Paper 1 Q26
26 Zoe and Amy are playing a board game.
- They each have one disc and take turns to roll a fair, ordinary dice.
- The player moves their disc clockwise the number of spaces shown on the dice.
- The winner is the first player whose disc is on HOME at the end of a turn.
Here is the board after Amy’s turn.
Work out the probability that Zoe wins within her next two turns. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((\text{P}(3) =)\ \dfrac{1}{6}\) or \((\text{P}(1, 2) =)\) or \((\text{P}(2, 1) =)\) \(\dfrac{1}{6} \times \dfrac{1}{6}\) or \(\dfrac{1}{36}\) | M1 | oe 3 on first roll or 1 on first roll and 2 on second or 2 on first roll and 1 on second |
| \(\dfrac{1}{6}\) and \(\dfrac{1}{6} \times \dfrac{1}{6}\) or \(\dfrac{1}{6}\) and \(\dfrac{1}{36}\) or \(\dfrac{1}{6} \times \dfrac{1}{6} \times 2\) or \(\dfrac{1}{36} \times 2\) or \(\dfrac{2}{6} \times \dfrac{1}{6}\) or \(\dfrac{2}{36}\) | M1dep | oe |
| \(\dfrac{1}{6} + \dfrac{1}{6} \times \dfrac{1}{6} \times 2\) or \(\dfrac{1}{6} + \dfrac{2}{36}\) | M1dep | oe |
| \(\dfrac{2}{9}\) or \(\dfrac{8}{36}\) or \(\dfrac{4}{18}\) | A1 | oe fraction, decimal or percentage |
Additional guidance
| For the first and second marks, do not allow \(\dfrac{1}{6}\) seen only as part of a multiplication string, but do allow it seen only in an addition | |
| For the first and second marks, do not allow \(\dfrac{1}{6} \times \dfrac{1}{6}\ (\times 2)\) or \(\dfrac{2}{6} \times \dfrac{1}{6}\) seen only as part of a longer multiplication string or in \(1 - \left(\dfrac{1}{6} \times \dfrac{1}{6}\right)\), but do allow them seen only in an addition | |
| Allow working in decimals rounded correctly to at least 2 dp for M marks, but answer must be given correctly as \(0.\dot{2}\) or \(22.\dot{2}\)% | |
| Ignore an incorrect simplification or conversion of a correct value | M1M1M1A1 |