© 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 If it is known that the number on the drawn card is
more than 3, what is the probability that it is an even number Solution Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is  greater than 3’