Higher June 2018 Paper 2 Q25
25 The Venn diagram shows some information about 150 students.
\(\xi\) = 150 students
C = students who study Chemistry
P = students who study Physics
The probability that a Physics student, chosen at random, also studies Chemistry is \(\dfrac{5}{12}\)
One of the 150 students is chosen at random.
Work out the probability that the student does not study either Chemistry or Physics. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{x}{x + 35} = \dfrac{5}{12}\) or \(\dfrac{35}{x + 35} = \dfrac{7}{12}\) or \(\dfrac{x}{35} = \dfrac{5}{7}\) or \(x : 35 = 5 : 7\) or links \(\dfrac{7}{12}\) to 35 | M1 | oe eg \(x + 35 = 60\) or links \(\dfrac{1}{12}\) to 5 |
| \(12x - 5x = 175\) or \(7x = 175\) or \(420 - 245 = 7x\) or (\(x =\)) 25 or \(\dfrac{25}{60}\) | M1dep | oe collects terms 25 may be seen in section labelled \(x\) on Venn diagram |
| (\(y =\)) \(150 - 47 - 35 -\) their 25 or 43 | M1dep | dep on M2 43 may be seen in section labelled \(y\) on Venn diagram |
| \(\dfrac{43}{150}\) or 0.286… or 0.287 or 0.29 or 28.6…% or 28.7% or 29% | A1 |
Additional guidance
| Accept \(\dfrac{7}{12} = 35\) | M1 |
| Ignore any incorrect cancelling or change of form (fraction, decimal or percentage) |