Higher November 2022 Paper 1 Q20
20 Alfie has 11 cards.
He has
3 blue cards
7 green cards
and 1 white card.
Alfie takes at random 2 of these cards.
Work out the probability that he takes cards of different colours. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{62}{110}\) | P1 | for process to find a probability of 2 cards of different colours, eg \(\dfrac{3}{11} \times \dfrac{7}{10}\) or \(\dfrac{3}{11} \times \dfrac{1}{10}\) or \(\dfrac{7}{11} \times \dfrac{3}{10}\) or \(\dfrac{7}{11} \times \dfrac{1}{10}\) or \(\dfrac{1}{11} \times \dfrac{3}{10}\) or \(\dfrac{1}{11} \times \dfrac{7}{10}\) oe or \(\dfrac{3}{11} \times \dfrac{8}{10}\) oe or \(\dfrac{7}{11} \times \dfrac{4}{10}\) oe or \(\dfrac{1}{11} \times \dfrac{10}{10}\) oe |
| P1 | for a complete process, eg \(\dfrac{3}{11} \times \dfrac{7}{10} + \dfrac{3}{11} \times \dfrac{1}{10} + \dfrac{7}{11} \times \dfrac{3}{10} + \dfrac{7}{11} \times \dfrac{1}{10} + \dfrac{1}{11} \times \dfrac{3}{10} + \dfrac{1}{11} \times \dfrac{7}{10}\) oe or \(\dfrac{3}{11} \times \dfrac{8}{10} + \dfrac{7}{11} \times \dfrac{4}{10} + \dfrac{1}{11} \times \dfrac{10}{10}\) oe | |
| A1 | for \(\dfrac{62}{110}\) oe | |
| OR | ||
| P1 | for process to find a probability of 2 cards of the same colour, eg \(\dfrac{3}{11} \times \dfrac{2}{10}\) or \(\dfrac{7}{11} \times \dfrac{6}{10}\) or \(\dfrac{1}{11} \times \dfrac{0}{10}\) oe | |
| P1 | for a complete process, eg \(1 - \dfrac{3}{11} \times \dfrac{2}{10} - \dfrac{7}{11} \times \dfrac{6}{10}\ \left(- \dfrac{1}{11} \times \dfrac{0}{10}\right)\) oe | |
| A1 | for \(\dfrac{62}{110}\) oe SC B1 for answer of \(\dfrac{62}{121}\) (replacement) |
Additional guidance
May see fraction with denominator 110
Accept equivalent fraction, decimal form 0.56(36…) or percentage form 56(.36…)%