Introduction:
When two dice are rolled, the sum of the numbers obtained on the two dice can vary from 2 to 12. In this question, we need to find the value of 'S' for which the probability of obtaining that sum is maximum.

Explanation:
To find the value of 'S' for which the probability is maximum, we need to analyze the possible outcomes and their corresponding probabilities.

1. Possible outcomes:
When two dice are rolled, the possible outcomes and their corresponding sums are as follows:
- Both dice show 1: Sum = 2
- One die shows 1 and the other shows 2: Sum = 3
- One die shows 1 and the other shows 3: Sum = 4
- ...
- Both dice show 6: Sum = 12

2. Counting the outcomes:
To find the probabilities, we need to count the number of outcomes for each sum 'S'. We can do this by listing all the possible outcomes and counting them.

3. Calculating the probabilities:
Once we have counted the number of outcomes for each sum 'S', we can calculate the probability of obtaining each sum. The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes.

4. Analysis:
To determine the value of 'S' for which the probability is maximum, we need to analyze the probabilities for each sum 'S' and identify the maximum probability.

5. Maximum probability:
The probability of obtaining each sum 'S' can be calculated using the formula:
Probability(S) = Number of outcomes for sum S / Total number of possible outcomes

6. Visualization:
We can represent the probabilities for each sum 'S' in a table or a graph to visualize the maximum probability.

Conclusion:
By calculating the probabilities for each sum 'S' and analyzing them, we can determine the value of 'S' for which the probability is maximum. The value of 'S' will depend on the number of outcomes for each sum and the total number of possible outcomes.