Now
P(B) =
6
216  and  P (A ∩ B) = 1
216
Then
P(A|B) =
1
P(A
B)
1
216
6
P(B)
6
216
∩
=
=
Example 6  A die is thrown twice and the sum of the numbers appearing is observed
to be 6 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