Solution We have 
4
P(A
B)
4
13
P(A|B)=
9
P(B)
9
13
∩
=
=
Example 2 A family has two children What is the probability that both the children are
boys given that at least one of them is a boy © NCERT
not to be republished
PROBABILITY      535
Solution Let b stand for boy and g for girl The sample space of the experiment is
S = {(b, b), (g, b), (b, g), (g, g)}
Let E and F denote the following events :
E : ‘both the children are boys’
F : ‘at least one of the child is a boy’
Then
E = {(b,b)} and F = {(b,b), (g,b), (b,g)}
Now
E ∩ F = {(b,b)}
Thus
P(F) = 3
4  and P (E ∩ F )= 1
4
Therefore
P(E|F) =
1
P(E
F)
1
34
P(F)
3
4
∩
=
=
Example 3  Ten cards  numbered 1 to 10 are placed in a box, mixed up thoroughly and
then one card is drawn randomly