NIMCET 2013 — Mathematics PYQ

When two fair dice are rolled, each die has 6 faces. Therefore, the total number of possible outcomes ($n(S)$) is:

Step 2: Identify Prime Numbers in the Range

The minimum sum possible is $1+1=2$ and the maximum sum is $6+6=12$.

The prime numbers between 2 and 12 are: 2, 3, 5, 7, and 11.

Step 3: Count Favorable Outcomes

We list the combinations for each prime sum:

• Sum is 2: $(1,1)$ — 1 outcome

• Sum is 3: $(1,2),(2,1)$ — 2 outcomes

• Sum is 5: $(1,4),(2,3),(3,2),(4,1)$ — 4 outcomes

• Sum is 7: $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$ — 6 outcomes

• Sum is 11: $(5,6),(6,5)$ — 2 outcomes

Total favorable outcomes ($n(E)$):

Step 4: Calculate Probability

The probability ($P$) is given by:

Now, simplify the fraction by dividing both numerator and denominator by 3:

Final Answer: The probability is $\frac{5}{12}$.