The correct answer is D.
Consider two cases:

Case i: The class consists of:
2 students born in January
2 students born in February,
2 students born in March
2 students born in April
.
.

2 students born in December
Now let's choose the first student at random.
At this point there are 23 students remaining.
1 of those 23 students was born in the same month as the first selected student, which means P(born in the same month) = 1/23
22 of those 23 students were born in a month different from the first selected student, which means P(born in different months) = 22/23
In this case, Quantity B is greater.


Case ii: The class consists of:
2 students born in January
2 students born in February,
2 students born in March
2 students born in April
.
.

2 students born in November
1,000,000,000,000 students born in December
In this case, it's pretty clear that the two selected students will probably be born in December.
Consequently, it's extremely unlikely that the two selected students will both be born in different months.
So, in this case, Quantity A is greater.

Answer: D