Higher November 2017 Paper 1 Q27
27 There are 11 pens in a box.
8 are black and 3 are red.
Two pens are taken out at random without replacement.
Work out the probability that the two pens are the same colour. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| (B, B) \(\dfrac{8}{11}\) and \(\dfrac{7}{10}\) or (R, R) \(\dfrac{3}{11}\) and \(\dfrac{2}{10}\) | M1 | oe may be seen on tree diagram |
| (B, B) \(\dfrac{8}{11} \times \dfrac{7}{10}\) or \(\dfrac{56}{110}\) or (R, R) \(\dfrac{3}{11} \times \dfrac{2}{10}\) or \(\dfrac{6}{110}\) | M1dep | oe may be seen on tree diagram |
| \(\dfrac{8}{11} \times \dfrac{7}{10} + \dfrac{3}{11} \times \dfrac{2}{10}\) | M1dep | \(\dfrac{56}{110} + \dfrac{6}{110}\) |
| \(\dfrac{62}{110}\) or \(\dfrac{31}{55}\) | A1 | oe fraction accept 0.56(…) or 56.(…)% |
| Alternative method 2 | ||
| (B, R) \(\dfrac{8}{11}\) and \(\dfrac{3}{10}\) or (R, B) \(\dfrac{3}{11}\) and \(\dfrac{8}{10}\) | M1 | oe may be seen on tree diagram |
| (B, R) \(\dfrac{8}{11} \times \dfrac{3}{10}\) or (R, B) \(\dfrac{3}{11} \times \dfrac{8}{10}\) or \(\dfrac{24}{110}\) | M1dep | oe may be seen on tree diagram |
| \(1 - \dfrac{8}{11} \times \dfrac{3}{10} - \dfrac{3}{11} \times \dfrac{8}{10}\) | M1dep | \(1 - \dfrac{24}{110} - \dfrac{24}{110}\) |
| \(\dfrac{62}{110}\) or \(\dfrac{31}{55}\) | A1 | oe fraction accept 0.56(…) or 56.(…)% |
Additional guidance
| Ignore incorrect simplification or conversion after a correct fraction | M3A1 |
| \(\dfrac{6820}{12\,100}\) | M3A1 |