Apps. and Interpretation for IBDP Maths Ebook 1 | Page 267

Exercise 75
1. Let C and D be independent events, with
0 < k < 0.5.
P( C) 2k
2
� and
P( D) � 3k
2
, where
(a) Write down an expression for P( C� D)
in terms of k .
(b) Given that P( C� D)=0.0096
, find k .
(c) Find P( C� D�)
.
(d) Find P( D� | C)
.
2. Let E and F be independent events, with
P( E) 4
3
� k and P( F)
(a) Write down an expression for P( E� F)
in terms of k .
(b)
Given that
(c) Find P( E� F)
.
1
P( E� F) = , find k .
2500
� k, where
[2]
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[2]
[2]
1
0 �k
� .
2
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3. Let A and B be independent events, with P( A) � 2k
and P( B) � 1.5P( A)
, where
0 < k < 0.5. It is given that P( A� B) � 6k
� 1.
(a)
Show that
P( A B) 6k
2
� � .
(b) Using P( A� B) � P( A) � P( B) � P( A� B)
, show that
(c) Hence, find the value of k .
(d) Find P( B| A ) .
2
6k
k 1 0
� � � .
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