Past papers › WAEC · 2017 · Private · General Maths · Paper 2 › Question 11 Question WAEC General Maths 2017 Theory Sets & Venn diagrams Probability Sets & Venn diagrams, Probability
WAEC 2017 · Paper 2 · Q11 Sets A = { x : 3 < x < 13 } A = \{x : 3 < x < 13\} A = { x : 3 < x < 13 } B = { x : 9 < x < 25 } B = \{x : 9 < x < 25\} B = { x : 9 < x < 25 } M = { multiples of 4 between 0 and 30 } M = \{\text{multiples of 4 between 0 and 30}\} M = { multiples of 4 between 0 and 30 } M M M
(a) (b) (c) Worked solution (try it first) List every set first.
M = { 4 , 8 , 12 , 16 , 20 , 24 , 28 } M = \{4, 8, 12, 16, 20, 24, 28\} M = { 4 , 8 , 12 , 16 , 20 , 24 , 28 } (7 numbers).
A A A is the members of
M M M between 3 and 13:
A = { 4 , 8 , 12 } A = \{4, 8, 12\} A = { 4 , 8 , 12 } .
B B B is those between 9 and 25:
B = { 12 , 16 , 20 , 24 } B = \{12, 16, 20, 24\} B = { 12 , 16 , 20 , 24 } .
(a) P ( A ) = 3 7 P(A) = \frac{3}{7} P ( A ) = 7 3 .
(b) B ′ B' B ′ is the members of
M M M not in
B B B :
{ 4 , 8 , 28 } \{4, 8, 28\} { 4 , 8 , 28 } .
P ( B ′ ) = 3 7 P(B') = \frac37 P ( B ′ ) = 7 3 .
(c) A ∪ B = { 4 , 8 , 12 , 16 , 20 , 24 } A \cup B = \{4, 8, 12, 16, 20, 24\} A ∪ B = { 4 , 8 , 12 , 16 , 20 , 24 } (12 counted once).
P ( A ∪ B ) = 6 7 P(A \cup B) = \frac67 P ( A ∪ B ) = 7 6 .
Watch out
A A A B B B M M M The inequalities are strict: 3 < x < 13 3 < x < 13 3 < x < 13 9 < x < 25 9 < x < 25 9 < x < 25 Report a problem with this question