Foundation January 2021 Paper 1R Q14
14 \(\mathscr{E} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}\)
\(A = \{2, 4, 6, 8, 10, 12\}\)
\(B = \{3, 6, 9, 12\}\)
(a) Complete the Venn diagram below for the sets \(\mathscr{E}\), \(A\) and \(B\).
One of the numbers in \(\mathscr{E}\) is to be chosen at random.
(b) Find the probability that this number is not in set \(A\) and not in set \(B\). (2)
| Scheme | Marks |
|---|---|
 Answer: Fully correct Venn diagram | B3 |
| (3) |
Notes
B3: fully correct Venn diagram
(B2 for 2 or 3 sections correct
B1 for 1 section correct)
| Scheme | Marks |
|---|---|
| M1 | |
| \(\dfrac{4}{12}\) | A1 |
| (2) | |
| (5 marks) |
Notes
M1: ft from (a)
\(\dfrac{\text{‘4’}}{a}\) where \(a \geqslant 4\) or \(\dfrac{b}{12}\) where \(b \leqslant 12\)
A1: oe