Question

When two dice are thrown simultaneously, what is the probability that the sum of the two numbers is less than 13?

• A. 1
• B. 1/12
• C. 1/6
• D. 1/12

Hint:

An event that is absolutely certain to happen always has a probability of exactly 1.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the probability of rolling a sum less than 13 when two standard six-sided dice are rolled together.


Step 2: Key Formula or Approach:
Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.


Step 3: Detailed Explanation:
When two standard dice are thrown, each die has faces numbered from 1 to 6.
The maximum possible sum occurs when both dice show their maximum face value, which is 6.
\[ \text{Maximum Sum} = 6 + 6 = 12 \] The possible sums range from 2 (1+1) to 12 (6+6).
Therefore, every single possible outcome of rolling two dice will result in a sum that is 12 or less.
This means that the condition "sum of the two numbers is less than 13" is always satisfied for every possible roll.
Since all 36 possible outcomes are favorable, the probability is:
\[ P(\text{Sum} < 13) = \frac{36}{36} = 1 \]

Step 4: Final Answer:
The probability is a certainty, which is 1.