Higher June 2018 Paper 2 Q13
13 Felix has 10 cards.
There are 5 red cards, 4 blue cards and 1 green card.
Felix takes at random one of the cards.
He does not replace the card.
Felix then takes at random a second card.
(a) Complete the probability tree diagram.
(b) Work out the probability that Felix takes at least one blue card and no green card. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{4}{9}, \dfrac{4}{9}, \dfrac{1}{9}, \dfrac{5}{9}, \dfrac{3}{9}, \dfrac{1}{9}, \dfrac{5}{9}, \dfrac{4}{9}, 0\) | B2oe |
| (2) |
Notes
B2oe: Award B1 for any 3 correct.
Decimals must be correct (recurring shown), 0 can be \(\dfrac{0}{9}\) or the branch crossed out or left blank
| Scheme | Marks |
|---|---|
| M1 | |
\(\dfrac{5}{10} \times \dfrac{4}{9} + \dfrac{4}{10} \times \dfrac{5}{9} + \dfrac{4}{10} \times \dfrac{3}{9}\) or \(\dfrac{5}{10} \times \dfrac{4}{9} + \dfrac{4}{10} \times \dfrac{8}{9}\) oe or \(1 - \left(\dfrac{5}{10} \times \dfrac{4}{9} + \dfrac{5}{10} \times \dfrac{1}{9} + \dfrac{4}{10} \times \dfrac{1}{9} + \dfrac{1}{10}\right)\) oe | M1 |
| \(\dfrac{52}{90}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: Award M1 for one correct product (ft tree diagram)
M1: A fully correct method (ft tree diagram)
A1: oe decimals 0.577… or 57.7...% rounded or truncated to 2 or more sf