What is the probability of getting a number greater than 6 on dice?

Question

What is the probability of getting a number greater than 6 on dice?

1. A. 1
2. B. 0.5
3. C. 0 (Correct answer)
4. D. 0.25

Correct Answer

Option C — 0

Detailed Solution & Explanation

The correct answer is 0.

Key Points

• A standard die has faces numbered 1, 2, 3, 4, 5, 6, so the sample space is $S = \{1,2,3,4,5,6\}$ with $n(S) = 6$.
• No face carries a number greater than 6, so the number of favourable outcomes is zero:
  • $P = \frac{0}{6} = \mathbf{0}$
• This is an impossible event — it cannot occur under any roll.

Additional Information

• Compare with the sure event in the preceding question: "a number less than 7" on the same die has probability 1, because all six outcomes qualify. The two questions are exact opposites built on the same sample space.
• Standard single-die probabilities:
  • Any specific number: $\frac{1}{6}$
  • An even number: $\frac{3}{6} = \frac{1}{2}$
  • A prime number (2, 3, 5): $\frac{3}{6} = \frac{1}{2}$
  • A number greater than 4: $\frac{2}{6} = \frac{1}{3}$