Analysis and Approaches for IBDP Maths Ebook 1 | Page 253

2. In a school, students are required to take at least one subject from art and technology. It is
known that 55 % of the students take art, and 70 % take technology.
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(a) Find the percentage of students who take both art and technology.
(b) Find the percentage of students who take one subject only.
At this school, 63 % of the students are male, and 72 % of the male take art.
[2]
[2]
(c)
A student is chosen at random. Let M be the event that the student is a male, and
let A be the event that the student takes art.
(d)
(i) Find P( M � A)
.
(ii) Show that M and A are not independent.
A female is chosen at random. Find the probability that she takes art.
[5]
[6]
3. In a class of 100 boys, 85 boys play football and 45 boys play rugby. Each boy must play
at least one sport from football and rugby.
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(a)
(b)
(c)
Find the percentage of boys who play both sports.
Find the percentage of boys who play only one sport.
One boy is selected at random.
[2]
[2]
(i)
(ii)
Given that the boy selected plays football, find the probability that he
plays rugby also.
Given that the boy selected plays only one sport, find the probability that
he plays rugby.
[4]
It is also given that 60% of the boys are taller than 180 cm and 90% of these boys play
football.
Let F be the event that a boy plays football and T be the event that a boy is taller than
180 cm.
(d) (i) Explain why F and T are not mutually exclusive.
(ii)
(iii)
Show that F and T are not independent.
Find the percentage of boys who is not taller than 180 cm and play
football.
[7]
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