Apps. and Interpretation for IBDP Maths Ebook 1 | Page 266

Your Practice Set – Applications and Interpretation for IBDP Mathematics
75
Paper 1 – 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)
.
(d) Find P( A� | B)
.
[2]
[2]
[2]
[2]
Solution
(a) P( A� B) � P( A) � P( B)
(b)
P( A B) k 2k
2
� � � (A1) for substitution
P( A B) 2k
3
� � A1 N2
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)
(d)
� � �� (A1) for substitution
2
2(0.3) 0.054 P( A B)
P( A��B) � 0.126
A1 N2
P( A��
B)
P( A� | B)
�
P( B)
0.126
P( A� | B)
� (A1) for substitution
2
2(0.3)
P( A� | B) � 0.7
A1 N2
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[2]
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