Statement -1 : A fair coin is tossed four times. The probability that heads exceed tails in number is `5/16`
Statement-2 : A fair coin is tossed, then the probability that it lands with heads is `1/2`

Options

A. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement -10
B. Statement-1 is true, Statement-2 is true, Statement-2 is Not a correct explanation for statement -10
C. Statement-1 is true, Statement-2 is False
D. Statement-1 is False, Statement-2 is true

Answer

To solve the problem, we will analyze both statements step by step.

### Step 1: Analyzing Statement 1
**Statement 1**: A fair coin is tossed four times. The probability that heads exceed tails in number is \( \frac{5}{16} \).

1. **Total Outcomes**: When a fair coin is tossed four times, the total number of outcomes is calculated as:
\[ n(S) = 2^4 = 16 \]
where \( n(S) \) is the total number of sample space outcomes.

2. **Event Definition**: Let \( E \) be the event that the number of heads exceeds the number of tails. This means we need to find the scenarios where the number of heads (H) is greater than the number of tails (T).

3. **Possible Outcomes**: The possible distributions of heads and tails when tossing the coin four times are:
- 4 heads, 0 tails (HHHH)
- 3 heads, 1 tail (HHHT, HHTH, HTHH, THHH)
- 2 heads, 2 tails (HHTT, HTHT, HTTH, THHT, THTH, TTHH)

We can see that:
- For 4 heads: 1 way
- For 3 heads: 4 ways
- For 2 heads: 6 ways (not counted since heads do not exceed tails)

Thus, the successful outcomes where heads exceed tails are:
- 4 heads: 1 way
- 3 heads: 4 ways

Total successful outcomes:
\[ n(E) = 1 + 4 = 5 \]

4. **Calculating Probability**: The probability \( P(E) \) that heads exceed tails is given by:
\[ P(E) = \frac{n(E)}{n(S)} = \frac{5}{16} \]

### Conclusion for Statement 1
Thus, Statement 1 is true.

### Step 2: Analyzing Statement 2
**Statement 2**: A fair coin is tossed, then the probability that it lands with heads is \( \frac{1}{2} \).

1. **Understanding Fair Coin**: A fair coin has two sides: heads (H) and tails (T). The probability of landing on either side is equal.

2. **Calculating Probability**: The probability of getting heads when tossing a fair coin is:
\[ P(H) = \frac{1}{2} \]

### Conclusion for Statement 2
Thus, Statement 2 is also true.

### Final Conclusion
Both statements are true, but Statement 2 does not explain why Statement 1 is correct. Therefore, the answer is that Statement 1 is true, Statement 2 is true, but Statement 2 is not a correct explanation for Statement 1.

### Final Answer
Option B: Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

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