Statement -1 : Let `E_1, E_2, E_3` be three events such that `P(E_1)+P(E_2)+P(E_3)=1, " then " E_1, E_2, E_3` are exhaustive events.
Statement-2 if the events `E_1, E_2 " and " E_3` be exhaustive events, then `P(E_1cupE_2cupE_3)=1`

Options

A. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement -9
B. Statement-1 is true, Statement-2 is true, Statement-2 is Not a correct explanation for statement -9
C. Statement-1 is true, Statement-2 is False
D. Statement-1 is False, Statement-2 is true

Answer

To solve the problem, we need to analyze both statements provided.

### Step-by-Step Solution:

**Step 1: Understanding Statement 1**
- Statement 1 claims that if \( P(E_1) + P(E_2) + P(E_3) = 1 \), then \( E_1, E_2, E_3 \) are exhaustive events.
- **Definition of Exhaustive Events:** Events are said to be exhaustive if their union covers the entire sample space. This means \( P(E_1 \cup E_2 \cup E_3) = 1 \).

**Step 2: Analyzing Statement 1**
- Given \( P(E_1) + P(E_2) + P(E_3) = 1 \), it does not necessarily imply that \( E_1, E_2, E_3 \) are exhaustive.
- For example, if \( P(E_1) = 0.5 \), \( P(E_2) = 0.4 \), and \( P(E_3) = 0.1 \), they add up to 1, but if there are other events in the sample space not accounted for by \( E_1, E_2, \) and \( E_3 \), then they are not exhaustive.

**Conclusion for Statement 1:**
- Therefore, Statement 1 is **false**.

**Step 3: Understanding Statement 2**
- Statement 2 states that if \( E_1, E_2, E_3 \) are exhaustive events, then \( P(E_1 \cup E_2 \cup E_3) = 1 \).
- Since exhaustive events cover the entire sample space, this statement is true by definition.

**Conclusion for Statement 2:**
- Therefore, Statement 2 is **true**.

### Final Conclusion:
- Statement 1 is false, and Statement 2 is true.