Analysis and Approaches for IBDP Maths Ebook 1 | Page 248

Your Practice Set – Analysis and Approaches for IBDP Mathematics
80
Paper 1 Section A – Probability Formulae
Example
Events A and B are independent with P( A� B) � P( A�
� B) � 0.1.
(a) Find P( B ) .
(b) Find P( A� B)
.
[2]
[4]
Solution
(a) P( B) � P( A� B) � P( A�
� B)
(M1) for valid interpretation
P( B) � 0.1� 0.1 � 0.2
A1 N2
[2]
(b) P( A� B) � P( A) � P( B)
(M1) for finding P( A )
0.1 �P( A) � 0.2
P( A) � 0.5
(A1) for correct value
P( A� B) � P( A) � P( B) � P( A� B)
(A1) for correct formula
P( A� B) � 0.5 � 0.2 �0.1 � 0.6
A1 N3
[4]
Exercise 80
1. Events A and B are independent with P( A�B) � 0.08 and P( A�B�) � 0.12 .
(a) Find P( A ) .
(b) Find P( A� B)
.
2. Events A and B are independent with P( A��B) � 0.15 and P( B) � 0.3 .
[2]
[4]
(a) Find P( A� B)
.
[2]
(b) Find P( A� B)
.
[4]
3. Events A and B are independent with P( A�B�) � 0.28 and P( A) � 0.4 . Find P( A� B)
.
[6]
4. Events A and B are independent with P( A�B) � 0.21 and P( A) � 0.7 . Find
P( A�� B�)
.
[7]
240
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