`A` and `B` are two non-mutually exclusive events. If `P(A)=1/4, P(B)=2/5` and `P(AuuB)=1/2` , find the values of `P(AnnB`) and `P(AuubarB )`

Explanation

To solve the problem, we need to find the values of \( P(A \cap B) \) and \( P(A \cup B') \) given the probabilities \( P(A) = \frac{1}{4} \), \( P(B) = \frac{2}{5} \), and \( P(A \cup B) = \frac{1}{2} \).

### Step 1: Use the formula for the union of two events
We start with the formula for the probability of the union of two events:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Substituting the known values:
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