If `P(A)=0.6,P(B)=0.5` and `P(A//B)=0.3`, then find `P(A uu B)`.

Answer

To find \( P(A \cup B) \) given \( P(A) = 0.6 \), \( P(B) = 0.5 \), and \( P(A | B) = 0.3 \), we can follow these steps:

### Step 1: Use the definition of conditional probability
The conditional probability \( P(A | B) \) is defined as:
\[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]
From the problem, we know \( P(A | B) = 0.3 \) and \( P(B) = 0.5 \). We can rearrange this formula to find \( P(A \cap B) \):
\[ P(A \cap B) = P(A | B) \times P(B) \]

### Step 2: Calculate \( P(A \cap B) \)
Substituting the known values:
\[ P(A \cap B) = 0.3 \times 0.5 = 0.15 \]

### Step 3: Use the formula for the union of two events
The formula for the probability of the union of two events \( A \) and \( B \) is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

### Step 4: Substitute the known values into the formula
Now we can substitute the values we have:
\[ P(A \cup B) = 0.6 + 0.5 - 0.15 \]

### Step 5: Calculate \( P(A \cup B) \)
Perform the addition and subtraction:
\[ P(A \cup B) = 1.1 - 0.15 = 0.95 \]

### Final Answer
Thus, the probability \( P(A \cup B) \) is:
\[ \boxed{0.95} \]