Question
Write $0.04628$ correct to 2 significant figures.
▶️Answer/Explanation
0.046 cao
The first 2 significant figures are 4 and 6.
the third digit (2). Since it’s less than 5, don’t round up.
$0.046$
Question
(a) In the Venn diagram, shade the region $M^{\prime}\cap N^{\prime}.$
(b) Find n$(B\cap(A^{\prime}\cup C)).$
▶️Answer/Explanation
(a) 
(b) $17$
(a)
\( M’ \) is the complement of set M, meaning everything outside of set M.
\( N’ \) is the complement of set N, meaning everything outside of set N.
The intersection of these complements, \( M’ \cap N’ \), represents the region that is outside both sets M and N .
(b)
\( B \cap (A’ \cup C) \) means the elements in set B that are also in the union of not A (A’) and set C.
Set A elements: 33, 16, 10, 18
Set B elements: 3, 16, 10, 4
Set C elements: 9, 18, 10, 4
Outside A elements (A’): 3, 4, 9, 20
\( A’ \cup C \):
This includes all elements outside A or in C:
Elements in A’: 3, 4, 9, 20
Elements in C: 9, 18, 10, 4
$
A’ \cup C = \{3, 4, 9, 10, 18, 20\}
$
Set B elements: 3, 16, 10, 4
Elements in both B and \( A’ \cup C \):
$
\{3, 10, 4\}
$
3 elements in B only → count: 3
10 elements in A ∩ B ∩ C → count: 10
4 elements in B ∩ C (not in A) → count: 4
Total count
$
3 + 10 + 4 = 17
$
Question
In the Venn diagram shade the region A ∪ B’
Answer/Explanation
Ans: 
Question
11 students are asked if they like rugby (R) and if they like football (F).
The Venn diagram shows the results.
(a) A student is chosen at random.
What is the probability that the student likes rugby and football?
(b) On the Venn diagram shade the region \(R’ \cap F’\).
Answer/Explanation
Ans:
(a) \(\frac{3}{11}\)
(b) 
Question
(a) n(\(\xi \)) = 10, n(A) = 7, n(B) = 6, n(\(A \cup B\))’, = 1.
(i) Complete the Venn diagram by writing the number of elements in each subset.
(ii) An element of is chosen at random.
Find the probability that this element is an element of \(A’ \cap B\).
(b) On the Venn diagram below, shade the region \(C’ \cap D’\).
Answer/Explanation
Ans:
(a) (i) 
(ii) \(\frac{2}{10}\) oe
(b) 