Analysis and Approaches for IBDP Maths Ebook 1 | Page 251

Front Page
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Paper 2 Section B – Miscellaneous problems
Example
In a school, students are required to learn at least one language, Japanese or Korean. It is
known that 80 % of the students learn Japanese, and 55 % learn Korean.
(a)
(b)
Find the percentage of students who learn both Japanese and Korean.
Find the percentage of students who learn Japanese, but not Korean.
[2]
[2]
At this school, 58 % of the students are female, and 75 % of the female learn Japanese.
(c)
A student is chosen at random. Let F be the event that the student is a female,
and let J be the event that the student learns Japanese.
(i) Find P( F� J)
.
18
(d)
(ii)
Show that F and J are not independent.
A male is chosen at random. Find the probability that he learns Japanese.
[5]
[6]
Solution
(a) P( J � K) � P( J) � P( K) � P( J � K)
(M1) for valid approach
1� 0.8� 0.55 � P( J�
K)
P( J�K) � 0.35
Thus, the required percentage is 35%. A1 N2
(b) P( J � K) � P( J � K�) � P( J)
(M1) for valid approach
0.35 � P( J� K�) � 0.8
P( J�K�) � 0.45
Thus, the required percentage is 45%. A1 N2
[2]
[2]
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