If A and B are two events such that `P(A)=0.3,P(B)=0.6` and `P(B//A)=0.5`, find `P(A//B)`.

Answer

To find \( P(A|B) \), we can use Bayes' theorem, which states:

\[ P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} \]

Given:
- \( P(A) = 0.3 \)
- \( P(B) = 0.6 \)
- \( P(B|A) = 0.5 \)

Now, we can substitute these values into the formula.

### Step 1: Substitute the known values into Bayes' theorem

\[ P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} = \frac{0.5 \cdot 0.3}{0.6} \]

### Step 2: Calculate the numerator

\[ 0.5 \cdot 0.3 = 0.15 \]

### Step 3: Divide the result by \( P(B) \)

\[ P(A|B) = \frac{0.15}{0.6} \]

### Step 4: Simplify the fraction

\[ P(A|B) = 0.25 \]

Thus, the final answer is:

\[ P(A|B) = 0.25 \]

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