Your Practice Paper – Applications and Interpretation SL for IBDP Mathematics
� 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) �
� Tree diagram : 1 . Path I : P ( A�B)
� pq
2 . Path I + Path III : �
P ( B) � P ( A� B) � P ( A�
� B)
� pq � ( 1 � p) r
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Discrete Probability Distributions
� Properties of a discrete random variable X :
X x
1 x
2 … x n
P ( X x)
� P ( X � x1
) X x2 1 . P ( X � x1) � P ( X � x2) � � P ( X � x n
) � 1
P ( � ) … P ( X � x n
)
2 . E ( X ) � x1P ( X � x1 ) � x2P ( X � x2) � � x P ( X � x ): Expected value of X 3 . E ( X ) � 0 if a fair game is considered n n
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