Higher November 2020 Paper 4 Q4
4 In a survey, 60 students were asked whether they have a bank account (B) and whether they have a part-time job (J).
The number of students who had neither a bank account nor a part-time job was \(x\).
The Venn diagram shows the results in terms of \(x\).
One of the 60 students is chosen at random.
Find the probability that they have a bank account.
Show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{20}{60}\) oe | 5 | B3 for \(x = 7\) OR B1 for \(x + 2x + x - 1 + 5x - 2\) or better M1 for simplifying their linear equation to the form \(ax + b = c\) or better e.g. \(9x - 3 = 60\) M1 for \(x = (60 + 3) \div 9\) AND M1 for \(\frac{\textit{their}\ 20}{60}\) If 0 scored SC1 for \(\frac{3x - 1}{60}\) | Equivalent includes \(\frac{1}{3}\), .333[..] and 33.3...% e.g. \(9x - 3\) their linear equation must include 60 FT their linear equation and show the steps to correctly solve it. third M1 FT their value of \(x\) so their 20 is their \((3x - 1)\) evaluated with their value of \(x\) |