ProbabilityTwo dice are rolled, find the probability that the sum is less than 13.Options1/213/41/4

1. Break Down the Problem

We need to find the probability that the sum of two rolled dice is less than 13.

2. Relevant Concepts

• The total number of outcomes when rolling two dice is $6 \times 6 = 36$.
• The possible sums when rolling two dice range from 2 (1+1) to 12 (6+6).

3. Analysis and Detail

• The only possible sums we can roll with two dice are 2 through 12.
• Therefore, since every possible outcome can only result in sums less than or equal to 12, all outcomes are valid for our probability condition where the sum is less than 13.

4. Verify and Summarize

• Total number of favorable outcomes (sum < 13) = Total outcomes (sum ranges from 2 to 12) = 36.
• Total possible outcomes = 36.

Final Answer

The probability that the sum of the two dice is less than 13 is given by:

$P(\text{sum} < 13) = \frac{36}{36} = 1$

Hence, the answer is 1 (which indicates that it is certain).