Question

What is the probability of getting a sum of 7 when two dice are rolled? 
 

• A. $\dfrac{1}{6}$
• B. $\dfrac{1}{12}$
• C. $\dfrac{1}{9}$
• D. $\dfrac{1}{36}$

Hint:

For dice probability, list all favorable outcomes systematically and divide by total possible outcomes (36 for two dice).

Answer 1

The Correct Option is A

- Step 1: Total outcomes when rolling two dice = $6 \times 6 = 36$.
- Step 2: Favorable outcomes for sum = 7: $(1, 6)$, $(2, 5)$, $(3, 4)$, $(4, 3)$, $(5, 2)$, $(6, 1)$. Total = 6.
- Step 3: Probability = $\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}} = \dfrac{6}{36} = \dfrac{1}{6}$.
- Step 4: Verify: Each pair is distinct and sums to 7. No other pairs work.
- Step 5: Check options: Option (a) is $\dfrac{1}{6}$, which matches.
- Step 6: Ensure no miscalculation in counting outcomes.