Question

If two dice are thrown together, find the probability that the sum of the appeared numbers on both dice is less than 7.

Hint:

List all possible outcomes systematically to count favorable cases correctly in dice-based probability problems.

Answer 1

Step 1: Total number of outcomes. 
Each die has 6 faces, so \[ \text{Total outcomes} = 6 \times 6 = 36 \] Step 2: Write possible sums less than 7. 
Sums: 2, 3, 4, 5, 6. 
Step 3: Count favorable outcomes. 

Total favorable outcomes = $1 + 2 + 3 + 4 + 5 = 15$. 
Step 4: Find probability. 
\[ P(\text{sum}<7) = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{15}{36} = \frac{5}{12} \] 
Step 5: Conclusion. 
Hence, the required probability = $\boxed{\dfrac{5}{12}}$.