Analysis and Approaches for IBDP Maths Ebook 1 | Page 252

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(c) (i) P( F�
J)
�P( J | F) � P( F)
(M1) for valid approach
�0.75� 0.58
(A1) for substitution
� 0.435
A1 N3
(ii) P( F) � P( J)
�0.58�
0.8
� 0.464
A1
� 0.435
R1
�P( F�
J)
Thus, F and J are not independent. AG N0
(d) P( F � J) � P( F�� J) � P( J)
(M1) for valid approach
0.435 � P( F�� J) � 0.8
(A1) for substitution
P( F��J) � 0.365
(A1) for correct value
P( F) �P( F�) � 1
0.58 �P( F�) � 1
P( F�) � 0.42
A1
P( J | F� )
P( F��
J)
�
P( F�)
(M1) for valid approach
0.365
�
0.42
� 0.869047619
� 0.869
A1 N3
[5]
[6]
Exercise 82
1. Consider the events A and B . It is given that P( A) � 0.4 , P( B) � 0.65 and
P( A�B) � 1.
(a) Find P( A� B)
.
(b) Find P( A�� B)
.
Consider another event C . It is also given that P( C) � 0.7 and P( AC� | ) 0.78 .
[2]
[2]
(c) (i) Find P( A� C)
.
(ii)
Show that A and C are not mutually exclusive.
(iii)
(d) Find P( C| A� ) .
Show that A and C are not independent.
[6]
[6]
244
SE Production Limited