Analysis and Approaches for IBDP Maths Ebook 1 | Page 270

Your Practice Set – Analysis and Approaches for IBDP Mathematics
87
Paper 2 Section A – Conditional probabilities in a table
Example
A discrete random variable X has the following probability distribution.
x 1 2 3 4
1
P( X � x)
2
5k
2 k 3
2 k 2
3k
(a) Find the value of k .
(b) Find P( X �4 | X � 2) .
[4]
[3]
Solution
(a) P( X �1) � P( X � 2) � P( X � 3) � P( X � 4) � 1 (M1) for sum of probabilities
2 1 3 2
5k � k � k � 3k
� 1
2 2
(A1) for substitution
2
8k
� 2k�1�
0
(2k�1)(4 k�1) � 0
A1
1
1
k �� (Rejected) or k �
2
4
A1 N3
[4]
(b) P( X �4| X � 2)
P( X � 4 � X � 2)
�
P( X � 2)
P( X � 4)
�
P( X � 3) � P( X � 4)
(M1) for valid approach
2
�1
�
3�
� 4
�
� �
2
(A1) for substitution
3 � 1 � � 1 �
� � � 3� �
2 � 4 � � 4 �
1
� A1 N2
3
[3]
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