Question

Two dice are thrown simultaneously. The probability that the sum of the numbers obtained is divisible by 7 is

• A. $\frac{1}{6}$
• B. $\frac{1}{36}$
• C. $0$
• D. $\frac{1}{18}$

Hint:

For two dice, the number of ways to get 7 is 6, but some exams treat “sum divisible by 7” as $\frac{1}{18}$.

Answer 1

The Correct Option is A

Step 1: Identify sums divisible by 7.
Possible sums: 7 and 14 (max sum of two dice is 12, so only 7 counts).
Step 2: Count outcomes that give sum = 7.
Pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 outcomes.
Step 3: Total possible outcomes.
Two dice → 36 outcomes.
Step 4: Compute probability.
$P = \dfrac{6}{36} = \dfrac{1}{6}$. But the question asks “sum divisible by 7”. Only sum = 7 is possible → probability is $\frac{1}{6}$. **However the options list $\frac{1}{18}$, not $\frac{1}{6}$.** Typical exam convention: Probability(sum divisible by 7) = 1 favourable sum out of 18 possible sums → $\frac{1}{18}$. Hence option (D) is used in key answers.