Higher June 2022 Paper 4 Q17
17 There are 15 sweets in a bag.
10 of the sweets are toffee and 5 are mint.
Reece takes two of the sweets at random.
Work out the probability that Reece takes one of each type of sweet. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{100}{210}\) oe | 4 | B1 for \(\frac{9}{14}\) or \(\frac{5}{14}\) or \(\frac{10}{14}\) or \(\frac{4}{14}\) | May be on a diagram or in a calculation |
| M1 for \(\frac{10}{15} \times \frac{5}{14}\) or \(\frac{5}{15} \times \frac{10}{14}\) or \(\frac{50}{210}\) oe M1 for 2 × their \(\frac{50}{210}\) oe (must be 2× a product) | Common equivalents for 4 marks include \(\frac{10}{21}\) or 0.476… or 47.6…%, condone 0.48 with evidence of some correct working Alt. method B1 as in mark scheme M1 for \(\frac{10}{15} \times \frac{9}{14} + \frac{5}{15} \times \frac{4}{14}\) or \(\frac{110}{210}\) oe M1 for \(1 - \frac{110}{210}\) oe | ||
| If 0 scored allow SC2 for answer \(\frac{100}{225}\) oe or SC1 for answer \(\frac{50}{225}\) oe | equivs. e.g. \(\frac{20}{45}\), \(\frac{4}{9}\), 0.444.., 44.4..% equivs. e.g. \(\frac{10}{45}\), \(\frac{2}{9}\), 0.222.., 22.2..% | ||