Assertion : Two coins are tossed. Number of elements in the sample space is 4.
Reason : When a coin is tossed n times then the number of elements in its sample space is n + 2.

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 evaluate the assertion and the reason given in the question.

### Step 1: Analyze the Assertion
The assertion states that when two coins are tossed, the number of elements in the sample space is 4.

1. **Understanding Sample Space**:
- When we toss a coin, there are two possible outcomes: Heads (H) or Tails (T).
- If we toss two coins, the possible outcomes can be represented as:
- HH (both coins show heads)
- HT (first coin shows heads, second coin shows tails)
- TH (first coin shows tails, second coin shows heads)
- TT (both coins show tails)
- Therefore, the total number of outcomes (elements in the sample space) when tossing two coins is 4.

**Conclusion for Step 1**: The assertion is **True**.

### Step 2: Analyze the Reason
The reason states that when a coin is tossed n times, the number of elements in its sample space is n + 2.

1. **Understanding Sample Space for n Tosses**:
- When a coin is tossed n times, the number of possible outcomes is given by the formula \(2^n\) (since each toss has 2 outcomes).
- For example:
- If n = 1 (1 toss), outcomes = \(2^1 = 2\)
- If n = 2 (2 tosses), outcomes = \(2^2 = 4\)
- If n = 3 (3 tosses), outcomes = \(2^3 = 8\)
- The formula \(n + 2\) does not correctly represent the number of outcomes. It is incorrect.

**Conclusion for Step 2**: The reason is **False**.

### Final Conclusion
- The assertion is True, while the reason is False. Therefore, the correct answer to the question is that the assertion is true, and the reason is false.

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