Higher January 2019 Paper 1R Q16
16 There are 12 beads in a bag.
7 of the beads are red.
3 of the beads are green.
2 of the beads are yellow.
Lucy takes at random a bead from the bag and keeps it.
Then Julian takes at random a bead from the bag.
(a) Work out the probability that they each take a yellow bead. (2)
(b) Work out the probability that the beads they take are not the same colour. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{2}{12} \times \dfrac{1}{11}\) | M1 |
| \(\dfrac{1}{66}\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| Any two of \(\dfrac{7}{12} \times \dfrac{3}{11} \left(= \dfrac{21}{132}\right)\) or \(\dfrac{7}{12} \times \dfrac{2}{11} \left(= \dfrac{14}{132}\right)\) or \(\dfrac{3}{12} \times \dfrac{2}{11} \left(= \dfrac{6}{132}\right)\) | M1 |
| \(2 \times \dfrac{7}{12} \times \dfrac{3}{11} + 2 \times \dfrac{7}{12} \times \dfrac{2}{11} + 2 \times \dfrac{3}{12} \times \dfrac{2}{11}\) | M1 |
| \(\dfrac{41}{66}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: for any two correct
M1: for a complete method
A1: oe
SC B2 for an answer of \(\dfrac{41}{72}\) oe
| Scheme | Marks |
|---|---|
| \(\dfrac{7}{12} \times \dfrac{6}{11} \left(= \dfrac{42}{132}\right)\) and \(\dfrac{3}{12} \times \dfrac{2}{11} \left(= \dfrac{6}{132}\right)\) | M1 |
| \(1 - \text{``}{\dfrac{2}{12} \times \dfrac{1}{11}}\text{''} - \dfrac{7}{12} \times \dfrac{6}{11} - \dfrac{3}{12} \times \dfrac{2}{11}\) | M1 |
| \(\dfrac{41}{66}\) | A1 |
Notes
M1: both correct
M1: for a complete method
SC B2 for an answer of \(\dfrac{41}{72}\) oe