4400 Higher November 2010 Paper 4 Q14
14 There are 9 beads in a bag.
4 of the beads are red.
3 of the beads are white.
2 of the beads are blue.
Sanjay takes at random a bead from the bag and does not replace it.
He then takes at random a second bead from the bag.
(a) Complete the probability tree diagram.
(b) Calculate the probability that one of Sanjay’s beads is red and his other bead is blue. (3)
| Scheme | Marks |
|---|---|
 | B3 |
| (3) |
Notes
B3: B1 \(\frac{3}{9}\) and \(\frac{2}{9}\) correct on LH branches
B2 All RH branches correct
(B1 one RH branch correct ie 3 probabilities)
| Scheme | Marks |
|---|---|
| \(\frac{4}{9} \times \frac{2}{8} + \frac{2}{9} \times \frac{4}{8}\) oe | M1 |
| M1 | |
| \(\frac{16}{72}\) or \(\frac{2}{9}\) oe | A1 |
| (3) | |
| (6 marks) |
Notes
M1: for \(\frac{4}{9} \times \text{“}\frac{2}{8}\text{”}\) or \(\text{“}\frac{2}{9}\text{”} \times \text{“}\frac{4}{8}\text{”}\) oe
M1: for sum of both products
A1: for \(\frac{16}{72}\) or \(\frac{2}{9}\) oe
M marks: award for correct use of probabilities (must be < 1) from their tree diagram.