It is given that,
2
×
2
Probability of even number = Probability of odd number
⇒
P
(
O
)
=
2
P
(
E
)
⇒
⇒
P
(
O
)
:
P
(
E
)
=
2
:
1
⇒
Probability of occurring odd number,
P
(
O
)
=
2
2
+
1
=
2
3
Probability of occurring odd number,
and probability of occurring 5each number,
P
(
E
)
=
1
2
+
1
=
1
3
and probability of occurring 5each number,
Now, G be the even that a number greater than 3 occur in a single roll of die.
So, the possible outcomes are 4, 5 and 6 out of which two are even and one odd.
∴
Required probability
=
P
(
G
)
=
2
×
P
(
E
)
×
P
(
O
)
∴
=
2
×
1
3
×
2
3
=
4
9
=