Assertion : Two well balanced dice are rolled and the numbers that turn up are observed. Then the number of elements in sample space is 12.
Reason : When two dice are rolled, number of elements in sample space is 6 x 6

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are tme but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the problem, we need to analyze the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that when two well-balanced dice are rolled, the number of elements in the sample space is 12.

### Step 2: Understand the Reason
The reason given states that when two dice are rolled, the number of elements in the sample space is calculated as \(6 \times 6\). This is because each die has 6 faces, and when rolling two dice, the outcomes can be represented as pairs of numbers (one from each die).

### Step 3: Calculate the Sample Space
To find the total number of outcomes when rolling two dice:
- For the first die, there are 6 possible outcomes (1 through 6).
- For the second die, there are also 6 possible outcomes (1 through 6).

Thus, the total number of outcomes in the sample space when rolling two dice is:
\[ 6 \times 6 = 36 \]

### Step 4: Conclusion
Since the assertion claims that the number of elements in the sample space is 12, which is incorrect, we conclude that the assertion is false. The reason, however, is correct as it accurately describes how to calculate the sample space for rolling two dice.

### Final Answer
- Assertion: False
- Reason: True