4MA0 Higher January 2015 Paper 3R Q22
22 Here are 7 cards.
Each card has a number on it.
Harry takes at random two cards.
(a) Calculate the probability that the numbers on the two cards are the same. (3)
(b) Calculate the probability that the sum of the numbers on the two cards is 5 (3)
| Scheme | Marks |
|---|---|
| \(\frac{2}{7} \times \frac{1}{6}\) or \(\frac{3}{7} \times \frac{2}{6}\) | M1 |
| \(\frac{2}{7} \times \frac{1}{6} + \frac{3}{7} \times \frac{2}{6}\) | M1 |
| \(\dfrac{8}{42}\) | A1 |
| (3) |
Notes
M1: Replacement - \(\frac{2}{7} \times \frac{2}{7}\) or \(\frac{3}{7} \times \frac{3}{7}\)
M1: Replacement - \(\frac{2}{7} \times \frac{2}{7} + \frac{3}{7} \times \frac{3}{7}\)
A1: \(\dfrac{8}{42}\) oe
| Scheme | Marks |
|---|---|
| \(\frac{2}{7} \times \frac{3}{6}\) or \(\frac{3}{7} \times \frac{2}{6}\) or \(\frac{1}{7} \times \frac{1}{6}\) | M1 |
| \(\frac{2}{7} \times \frac{3}{6} + \frac{3}{7} \times \frac{2}{6} + \frac{1}{7} \times \frac{1}{6} + \frac{1}{7} \times \frac{1}{6}\) | M1 |
| \(\dfrac{14}{42}\) | A1 |
| (3) | |
| (6 marks) |
Notes
M1: Replacement –
\(\frac{2}{7} \times \frac{3}{7}\) or \(\frac{3}{7} \times \frac{2}{7}\) or \(\frac{1}{7} \times \frac{1}{7}\)
M1: Replacement - \(\frac{2}{7} \times \frac{3}{7} + \frac{3}{7} \times \frac{2}{7} + \frac{1}{7} \times \frac{1}{7} + \frac{1}{7} \times \frac{1}{7}\)
A1: \(\dfrac{14}{42}\) oe