Analysis and Approaches for IBDP Maths Ebook 1 | Page 249

Front Page
81
Paper 2 Section A – Setting up probability equations
Example
Let A and B be independent events, with P( A)
� k and
P( B) 2
2
� k , where 0 < k < 0.5.
(a) Write down an expression for P( A� B)
in terms of k .
(b) Given that P( A� B)=0.054
, find k .
(c) Find P( A� | B)
.
[2]
[2]
[3]
Solution
(a) P( A�
B)
�P( A) � P( B)
2
�k� 2k
(A1) for substitution
3
� 2k
A1 N2
(b)
3
2k � 0.054
(A1) for correct equation
3
k � 0.027
k � 0.3
A1 N2
(c) P( B) � P( A� B) � P( A�
� B)
2
2(0.3) � 0.054 � P( A�
� B)
(A1) for substitution
P( A��B) � 0.126
P( A�
| B)
P( A��
B)
�
P( B)
0.126
�
2
2(0.3)
(A1) for substitution
� 0.7
A1 N2
[2]
[2]
[3]
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