Question

If there are two red and blue dice. Find the probability when the sum of the dice is a prime number, where the number on red is more than blue.

• A. 1/12
• B. 5/36
• C. 7/36
• D. 1/9

Hint:

Use the prime sums $3,5,7,11$. Because the dice have colours, keep ordered pairs and impose red greater than blue before dividing by $36$.

Answer 1

The Correct Option is B

Concept:

• Fix the red-die value and list only smaller blue values that produce a prime sum.
• Each ordered pair has probability $1/36$.

Step 1: Check red values $1,2,3$.
The valid pairs are $(2,1)$ and $(3,2)$, giving $2$ outcomes.

Step 2: Check red values $4,5,6$.
The valid pairs are $(4,1),(4,3),(5,2),(6,1),(6,5)$, giving $5$ more outcomes.

Step 3: Form the probability.
There are $2+5=7$ favourable outcomes among $36$ equally likely outcomes.

Final Answer: $\dfrac{7}{36}$, option C