Find P(A/B) , is P (B) =0.5 and `P (A cap B)` =0.32

Answer

To find \( P(A|B) \), we will use the formula for conditional probability:

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

### Step 1: Identify the given values
We are given:
- \( P(B) = 0.5 \)
- \( P(A \cap B) = 0.32 \)

### Step 2: Substitute the values into the formula
Now we substitute the values into the formula:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.32}{0.5} \]

### Step 3: Simplify the fraction
To simplify \( \frac{0.32}{0.5} \), we can multiply the numerator and the denominator by 10 to eliminate the decimal:

\[ P(A|B) = \frac{0.32 \times 10}{0.5 \times 10} = \frac{3.2}{5} \]

### Step 4: Further simplify the fraction
Next, we can convert \( \frac{3.2}{5} \) into a fraction:

\[ P(A|B) = \frac{32}{50} \]

### Step 5: Reduce the fraction to its simplest form
Now, we can reduce \( \frac{32}{50} \):

\[ P(A|B) = \frac{32 \div 2}{50 \div 2} = \frac{16}{25} \]

### Final Answer
Thus, the final answer is:

\[ P(A|B) = \frac{16}{25} \]

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