Statement -1 : if the odds against an event is `2/3`, then probability of occuring of the event is `3/5`.
Statement-2 : For two events A and B, `P(A'capB')=1-P(AcupB).`

Options

A. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement -2
B. Statement-1 is true, Statement-2 is true, Statement-2 is Not a correct explanation for statement -2
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 evaluate the two statements given:

### Statement 1:
If the odds against an event are \( \frac{2}{3} \), then the probability of the event occurring is \( \frac{3}{5} \).

**Step 1: Understanding Odds Against an Event**
- The odds against an event \( A \) are given as \( \frac{m}{n} \), where \( m \) is the number of unfavorable outcomes and \( n \) is the number of favorable outcomes.
- Here, the odds against the event are \( \frac{2}{3} \), meaning there are 2 unfavorable outcomes and 3 favorable outcomes.

**Step 2: Total Outcomes**
- The total number of outcomes \( = m + n = 2 + 3 = 5 \).

**Step 3: Probability of the Event**
- The probability of the event \( A \) occurring is given by:
\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{5} \]
- Thus, Statement 1 is **true**.

### Statement 2:
For two events \( A \) and \( B \), \( P(A' \cap B') = 1 - P(A \cup B) \).

**Step 4: Understanding the Complement of Events**
- The complement of event \( A \) is denoted as \( A' \) and represents all outcomes not in \( A \).
- The intersection \( A' \cap B' \) represents the outcomes that are neither in \( A \) nor in \( B \).

**Step 5: Using the Complement Rule**
- According to the complement rule in probability:
\[ P(A' \cap B') = 1 - P(A \cup B) \]
- This is a fundamental property of probabilities, confirming that Statement 2 is also **true**.

### Conclusion:
Both statements are true, but Statement 2 does not serve as a correct explanation for Statement 1.

### Final Answer:
Both Statement 1 and Statement 2 are true, but Statement 2 is not a correct explanation for Statement 1.

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