Higher June 2018 Paper 3 Q27
27 A bag contains 30 discs.
10 are red and 20 are blue.
One disc is taken out at random and replaced by two of the other colour.
Another disc is then taken out at random and replaced by two of the other colour.
Another disc is then taken out at random.
Work out the probability that all three discs taken out are red. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{10}{30}\) and \(\dfrac{9}{31}\) seen or \(\dfrac{1}{3}\) and \(\dfrac{9}{31}\) seen | M1 | oe accept 0.33… and 0.29… |
| \(\dfrac{10}{30} \times \dfrac{9}{31} \times \dfrac{8}{32}\) or \(\dfrac{1}{3} \times \dfrac{9}{31} \times \dfrac{1}{4}\) | M1dep | oe accept 0.33… and 0.29… and 0.25 |
| \(\dfrac{3}{124}\) or [0.0239, 0.0242] | A1 | oe eg \(\dfrac{720}{29\,760}\) |
Additional guidance
| Fractions do not have to be in simplest form | |
| \(\dfrac{10}{30} \times \dfrac{9}{31} \times \dfrac{8}{32} \times \dfrac{7}{33}\) | M1M0 |
| \(\dfrac{10}{30} + \dfrac{9}{31} + \dfrac{8}{32}\) | M1M0 |