Higher June 2022 Paper 3 Q17
17 In a video game, players make their own character.
They choose one of each from
8 faces
4 bodies
5 hairstyles.
(a) How many different characters can be made? [2 marks]
(b) Two characters are made at random.
What is the probability that they are exactly the same? [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(8 \times 4 \times 5\) | M1 | |
| 160 | A1 |
Additional guidance
| \(\dfrac{1}{8} \times \dfrac{1}{4} \times \dfrac{1}{5} = 160\) (recovered) | M1A1 |
| \(\dfrac{1}{8} \times \dfrac{1}{4} \times \dfrac{1}{5}\) | M0A0 |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{1}{160}\) or 0.00625 or 0.625% or \(6.25 \times 10^{-3}\) | B1ft | oe fraction, decimal or percentage ft \(\dfrac{1}{\text{their answer to (a)}}\) |
Additional guidance
| Accept decimal or percentage answers rounded to 2 sf or better for ft eg ft 17 gives 0.058823529… so accept 0.059 or better | |
| Ignore an attempt to convert a fraction to a decimal or round a decimal or percentage after a correct value is seen | |
| 1 : 160 or 1 in 160 or 1 out of 160 | B0 |
| \(\dfrac{1}{160} + \dfrac{1}{160} = \dfrac{2}{320} = \dfrac{1}{160}\) | B0 |
| \(\dfrac{1}{160} \times \dfrac{1}{160} = \dfrac{2}{320} = \dfrac{1}{160}\) | B0 |