15 \(\mathscr{E} = \{\)odd numbers less than 30\(\}\) \(A = \{3, 9, 15, 21, 27\}\) \(B = \{5, 15, 25\}\)
(a) Complete the Venn diagram to represent this information.(4)
A number is chosen at random from the universal set, \(\mathscr{E}\).
(b) What is the probability that the number is in the set \(A \cup B\)? (2)
Mark scheme (a)
Working
Answer
Mark
Notes
Venn Diagram
B1
for labels on diagram
M1
for just 15 in the intersection
M1
for just 5 and 25 in only set B or just 3, 9, 21 and 27 in only set A or just 1, 7, 11, 13, 17, 19, 23, 29 in \((A \cup B)\)′
C1
for all numbers correctly placed in the Venn Diagram Ignore all entries except the region you are marking for each method mark
Mark scheme (b)
Answer
Mark
Notes
\(\dfrac{7}{15}\)
P1
ft for \(\dfrac{\text{``}7\text{''}}{a}\) where \(a \geqslant \text{``}7\text{''}\) or \(\dfrac{b}{\text{``}15\text{''}}\) where \(b \leqslant \text{``}15\text{''}\)
