Foundation June 2019 Paper 3 Q24

EdexcelCurrent spec5 marksBasic Probability Sets

24 \(\mathscr{E} = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}\)
\(A = \{1, 5, 6, 8, 9\}\)
\(B = \{2, 6, 9\}\)

An empty Venn diagram: two overlapping ovals A and B inside a rectangle labelled with the universal set symbol

(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)

Completed Venn diagram: 1, 5, 8 in A only; 6 and 9 in the intersection; 2 in B only; 3, 4, 7 outside both circles — Mark scheme (a)

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

Mark scheme (b)

Answer	Mark	Mark scheme
\(\dfrac{2}{9}\)	M1	ft for identification of 2 or 9 or ft diagram
\(\dfrac{2}{9}\)	A1	\(\dfrac{2}{9}\) oe or ft diagram

Additional guidance

For the M1: 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

For the A1: Accept any equivalent fraction, decimal form 0.22(22..) or percentage form 22(.22...)%