UGC NET Questions (Paper – 1)

When two fair dice are thrown, there are 6 × 6 = 36 equally likely outcomes. A sum greater than 9 corresponds to sums of 10, 11 and 12. The sum 10 can occur in 3 ways, 11 in 2 ways and 12 in 1 way, giving a total of 6 favourable outcomes. The probability is therefore 6/36, which simplifies to 1/6. This fraction represents the chances of obtaining a sum greater than 9 on a single throw of two dice.

Option A:
Option A, 1/18, undercounts the favourable outcomes and would require only 2 favourable cases out of 36, which is not the case here. It might arise from only considering one of the sums.

Option B:
Option B, 1/9, simplifies to 4/36 and still does not match the 6 favourable cases actually present in the sample space. It underestimates the event’s likelihood.

Option C:
Option C, 5/36, suggests only 5 favourable outcomes, but a systematic list shows there are 6 outcome pairs producing sums 10, 11 and 12.

Option D:
Option D, 1/6, correctly reflects the 6 favourable outcomes out of 36 total and is the simplified probability consistent with the complete sample space.