Two dice are thrown simultaneously and the sum of the numbers which come up on the dice is noted. Consider the following events
A = The sum is even
B = The sum is a multiple of 3
C = The sum is less than 4
D = The sum is greater than 11
Which of the following is/are elementary event(s)?

Options

A. A and B
B. A and C
C. Only C
D. Only D

Answer

To determine which of the events A, B, C, and D are elementary events when two dice are thrown, we need to analyze each event based on the outcomes of the sums of the numbers on the dice.

### Step-by-Step Solution:

1. **Total Outcomes**:
When two dice are thrown, the total number of possible outcomes is \(6 \times 6 = 36\).

2. **Event A: The sum is even**:
The possible sums when rolling two dice range from 2 to 12. The even sums are 2, 4, 6, 8, 10, and 12. We need to find all combinations that yield these sums:
- Sum = 2: (1,1)
- Sum = 4: (1,3), (2,2), (3,1)
- Sum = 6: (1,5), (2,4), (3,3), (4,2), (5,1)
- Sum = 8: (2,6), (3,5), (4,4), (5,3), (6,2)
- Sum = 10: (4,6), (5,5), (6,4)
- Sum = 12: (6,6)

Counting all combinations, we find there are 18 outcomes. Since there are multiple outcomes, **Event A is not an elementary event**.

3. **Event B: The sum is a multiple of 3**:
The multiples of 3 within the range of possible sums (2 to 12) are 3, 6, 9, and 12. We find combinations for these sums:
- Sum = 3: (1,2), (2,1)
- Sum = 6: (1,5), (2,4), (3,3), (4,2), (5,1)
- Sum = 9: (3,6), (4,5), (5,4), (6,3)
- Sum = 12: (6,6)

Counting these, we find there are 12 outcomes. Since there are multiple outcomes, **Event B is not an elementary event**.

4. **Event C: The sum is less than 4**:
The sums less than 4 are 2 and 3. The combinations are:
- Sum = 2: (1,1)
- Sum = 3: (1,2), (2,1)

Counting these, we find there are 3 outcomes. Since there are multiple outcomes, **Event C is not an elementary event**.

5. **Event D: The sum is greater than 11**:
The only sums greater than 11 are 12. The combinations are:
- Sum = 12: (6,6)

There is only 1 outcome. Since there is only one outcome, **Event D is an elementary event**.

### Conclusion:
The only elementary event among the given options is **Event D**.