Higher June 2019 Paper 3 Q1
1 \(\mathscr{E} = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}\)
\(A = \{1, 5, 6, 8, 9\}\)
\(B = \{2, 6, 9\}\)
(a) Complete the Venn diagram to represent this information. (3)
A number is chosen at random from the universal set \(\mathscr{E}\).
(b) Find the probability that the number is in the set \(A \cap B\) (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| 6, 9 1, 5, 8 2 3, 4, 7 | M1 | for 6, 9 in the intersection only |
| M1 | for 1, 5, 8 in set \(A\) only or 2 in set \(B\) only or 3, 4, 7 in set \((A \cup B)'\) only | |
| C1 | for all numbers correctly placed in the Venn Diagram |
Additional guidance
Ignore all entries except the region you are marking for each method mark
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{2}{9}\) | M1 | ft for identification of 2 or 9 or ft diagram |
| A1 | \(\dfrac{2}{9}\) oe or ft diagram |
Additional guidance
Need not be written in correct form at this stage eg could be a ratio 2 : 9
Repeated digits in the diagram should be counted as 2 elements
Accept any equivalent fraction, decimal form 0.22(22..) or percentage form 22(.22…)%