Correct Answer - D
In the 22nd century there are 25 leap years viz. 2100, 2104,.., 2196 and 75 non-leap years.
Consider the following events :
E
1
E
= Selecting a leap year 22nd century
E
2
E
= Selecting a non-leap year from 22nd century
A=There are 53 Sundays in a year of 22nd century
We have,
P
(
E
1
)
=
25
100
,
P
(
E
2
)
=
75
100
P
P
(
A
/
E
1
)
=
2
7
and
P
(
A
/
E
2
)
=
1
7
P
Required probability =P(A)
=
P
(
(
A
∩
E
1
)
∪
(
A
∩
E
2
)
)
=
=
P
(
A
∩
E
1
)
+
P
(
A
∩
E
2
)
=
=
P
(
E
1
)
P
(
A
/
E
1
)
+
P
(
E
2
)
P
(
A
/
E
2
)
=
=
25
100
×
2
7
+
75
100
×
1
7
=
5
28
=
