Higher November 2018 Unit 2 Q15
15.
(a) Three unbiased 6-sided dice are rolled at the same time.
Calculate the probability they will all land on a 5. [2]
Calculate the probability they will all land on a 5. [2]
(b) Four unbiased 6-sided dice are now rolled.
Calculate the probability that at least three of the dice will land on a 5. [4]
Calculate the probability that at least three of the dice will land on a 5. [4]
| Scheme | Marks | Comments |
|---|---|---|
| \(\tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{1}{6}\) | M1 | |
| \(= \tfrac{1}{216}\) or equivalent. ISW | A1 | Allow decimal equivalents 0.004(6…) OR 0.005 OR corresponding percentage values. Unsupported decimal answer of 0.0046(…) gains both marks. |
| Scheme | Marks | Comments |
|---|---|---|
| Sight of \(\tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \quad \left(= \tfrac{1}{1296}\right)\) | B1 | |
| Sight of \(\tfrac{5}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \times 4 \quad \left(= \tfrac{20}{1296} \text{ or } \tfrac{5}{324}\right)\) | B2 | B1 for sight of \(\tfrac{5}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \; \left(= \tfrac{5}{1296}\right)\) |
| \(\left(\tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} + \tfrac{5}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \times 4 =\right)\) \(\tfrac{21}{1296} \qquad \left(= \tfrac{7}{432}\right)\) ISW. | B1 | CAO. NB: sight of \(\tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{6}{6} \; \left(= \tfrac{6}{1296}\right)\) gains B1B1, but \(\tfrac{1}{6} \times \tfrac{1}{6} \times \tfrac{1}{6} \left(= \tfrac{1}{216}\right)\) gains B0. |