What is the conditional probability that the number 4 has appeared at least
once Solution  Let E be the event that ‘number 4 appears at least once’ and F be the event
that ‘the sum of the numbers appearing is 6’ Then,
E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4), (5,4), (6,4)}
and
F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have
P(E) = 11
36 and P(F) = 5
36
Also
E∩F = {(2,4), (4,2)}
© NCERT
not to be republished
PROBABILITY      537
Therefore
P(E∩F) =
2
36
Hence, the required probability
P(E|F) =
2
P(E
F)
2
536
P(F)
5
36
∩
=
=
For the conditional probability discussed above, we have considered the elemen-
tary events of the experiment to be equally likely and the corresponding definition of
the probability of an event was used However, the same definition can also be used in
the general case where the elementary events of the sample space are not equally
likely, the probabilities P(E∩F) and P(F) being calculated accordingly