the sample points of E ∩ F © NCERT
not to be republished
PROBABILITY      533
Thus, we can also write the conditional probability of E given that F has occurred as
P(E|F) =
Numberof elementaryeventsfavourableto E
F
Numberof elementaryeventswhicharefavourableto F
∩
=
(E
(F)F)
n
n
∩
Dividing the numerator and the denominator by total number of elementary events
of the sample space, we see that P(E|F) can also be written as
P(E|F) =
(E
F)
P(E
F)
(S)
(F)
P(F)
(S)
n
nn
n
∩
∩
= (1)
Note that (1) is valid only when P(F) ≠ 0 i e