Higher November 2022 Paper 2 Q14
14. Dora has two boxes, \(A\) and \(B\).
The boxes contain beads which are identical in shape.
Box \(A\) contains 9 green, 6 red and 5 yellow beads.
Box \(B\) contains 12 red and 8 yellow beads.
Dora takes a bead at random from box \(A\). If the bead is:
- green, she puts it back in box \(A\)
- red or yellow, she puts it in box \(B\).
She then takes a bead at random from box \(B\).
(a) Complete the tree diagram. [3]

(b) Find the probability that Dora takes two beads of the same colour. [3]
| Scheme | Marks | Comments |
|---|---|---|
Correct tree diagram e.g.![]() | B3 | B1 for each pair of branches correct Allow equivalent fractions in all cases. |
| Scheme | Marks | Comments |
|---|---|---|
| \(\left(\dfrac{6}{20}\times\dfrac{13}{21}\right) + \left(\dfrac{5}{20}\times\dfrac{9}{21}\right)\) oe | M2 | Check tree diagram FT ‘their probabilities’ for M2 or M1, providing at least B1 awarded in (a) M1 for sight of one correct product |
| \(\dfrac{123}{420}\) or \(\dfrac{41}{140}\) oe, ISW | A1 | FT ‘their tree diagram’ |
| (6) |
