Say True or False giving reasons:
(i) `P(A)=1/3,P(B)=2/3, A` and B are mutually exclusive and exhaustive
(ii) `P(A)=0.4, P(B)=0.25,` P(A orB)=0.65.
A and B are mutually exclusive events.
(iii)P(A)=0.3, P(B)=.45, P(A and B) =0.2, A and B are not mutually exclusive events.
(iv) P(A)=0.35, P(B)=0.65, A and B are complementary events.

Answer

Let's analyze each part of the question step by step to determine if the statements are true or false, along with the reasons.

### Part (i):
**Statement**: `P(A) = 1/3, P(B) = 2/3, A and B are mutually exclusive and exhaustive.`

**Solution**:
1. **Mutually Exclusive**: Events A and B are mutually exclusive if \( P(A \cap B) = 0 \).
2. **Exhaustive**: Events A and B are exhaustive if \( P(A \cup B) = 1 \).
3. Calculate \( P(A \cup B) \):
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{1}{3} + \frac{2}{3} - 0 = 1 \]
4. Since \( P(A \cap B) = 0 \) and \( P(A \cup B) = 1 \), A and B are indeed mutually exclusive and exhaustive.

**Conclusion**: True.