Higher January 2021 Paper 2R Q16
16 Two events \(A\) and \(B\) are such that \(\mathrm{n}(A) = 62 \quad \mathrm{n}(B) = 30\) and \(\mathrm{n}(A \cup B) = 68\)
Given that \(\mathrm{n}(\mathscr{E}) = 80\)
(a) complete the Venn diagram to show the number of elements in each region.
An element is chosen at random from \(\mathscr{E}\).
(b) Using the Venn diagram, find the probability that this element is in
(i) \(A \cap B\) (1)
(ii) \(A \cup B'\) (2)
| Scheme | Marks |
|---|---|
 Answer: 12, 38, 24, 6 | B2 |
| (2) |
Notes
B2: B2 for all 4 correct values, in correct regions.
B1 for 2 or 3 correct values in correct regions
| Scheme | Marks |
|---|---|
(i) Answer: \(\dfrac{24}{80}\) oe | B1ft |
| (ii) eg 62 + “12” or 80 – “6” oe | M1ft |
| \(\dfrac{74}{80}\) oe | A1 ft |
| (3) | |
| (5 marks) |
Notes
B1ft: 0.3 ft their 24
M1ft: A complete method to find the number of elements in the required set.
A1 ft: 0.925
Penalise incorrect probability notation once only