P(B)
(C) P(B|A) > P(B)
(D) P(B|A) = P(B)
19 If A and B are any two events such that P(A) + P(B) – P(A and B) = P(A), then
(A) P(B|A) = 1
(B) P(A|B) = 1
(C) P(B|A) = 0
(D) P(A|B) = 0
© NCERT
not to be republished
PROBABILITY      585
Summary
The salient features of the chapter are –
� The conditional probability of an event E, given the occurrence of the event F
is given by 
P(E
F)
P(E | F)
P(F)
∩
=
, P(F) ≠ 0
� 0 ≤ P (E|F) ≤ 1,
P (E′|F) = 1 – P (E|F)
P ((E ∪ F)|G) = P (E|G) + P (F|G) – P ((E ∩ F)|G)
� P (E ∩ F) = P (E) P (F|E), P (E) ≠ 0
P (E ∩ F) = P (F)  P (E|F), P (F) ≠ 0
� If E and F are independent, then
P (E ∩ F) = P (E) P (F)
P (E|F) = P (E), P (F) ≠ 0
P (F|E) = P (F), P(E) ≠ 0
� Theorem of total probability
Let {E1, E2, ,En) be a partition of a sample space and suppose that each of
E1, E2, , En has nonzero probability