To find the probability that the sum of the numbers on two six-sided dice is 5, follow these steps:

Step 1: Determine the total number of outcomes.

Each die has 6 faces, so the total number of outcomes when rolling two dice is: $6 \times 6 = 36$

Step 2: Identify the favorable outcomes.

To achieve a sum of 5, the following pairs of numbers on the two dice are possible:

• (1, 4)
• (2, 3)
• (3, 2)
• (4, 1)

There are 4 favorable outcomes.

Step 3: Calculate the probability.

The probability is the ratio of the number of favorable outcomes to the total number of outcomes: $\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{36} = \frac{1}{9}$

Final Answer:

The probability that the sum of the numbers on the two dice is 5 is $\frac{1}{9}$.

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Would you like more details or have any other questions? Here are some related questions you might find interesting:

1. What is the probability that the sum is 7 when rolling two dice?
2. What is the probability that the sum is less than 5?
3. What is the probability that the sum is greater than 8?
4. What is the probability of rolling a sum of 2 or 12 with two dice?
5. What is the probability that both dice show the same number (doubles)?

Tip: When calculating probabilities involving sums of dice, listing all possible combinations that meet the criteria can be very helpful.