Your Practice Paper – Analysis and Approaches HL for IBDP Mathematics
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Permutations and Combinations
� Permutations and combinations when a sample of r objects are selected from a set of n objects , 0 �r� n:
1 .
2 . n n! Pr
� : Number of permutations when the order is taken into ( n� r)! account n �n� n!
Cr �� ��
: Number of combinations when the order is not
�r � r!( n � r)! taken into account
26 Probability
� Terminologies :
1 . U : Universal set 2 . A : Event 3 . x : Outcome of an event 4 . nU ( ): Total number of elements
5 . nA ( ): Number of elements in A
� Formulae for probability : 1 . P ( A� B) � P ( A) � P ( B) � P ( A�
B)
2 . P ( A�) �1� P ( A)
3 .
P ( A� B)
P ( A| B) �
P ( B) 4 . P ( A) � P ( A� B) � P ( A�
B�)
5 . P ( A�� B�) � P ( A� B) � 1 6 . P ( A� B) � P ( A) � P ( B) and P ( A�B) � 0 if A and B are mutually exclusive
7 . P ( A� B) � P ( A) � P ( B) and P ( A| B) � P ( A) if A and B are independent
� Venn diagram :
1 . Region I : A�
B
2 . Region II : A�
B� 3 . Region III : A��
B 4 . Region IV : ( A�
B) �
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