If `P(A) =1/2 ,P(B) =3/5 and P (A cap B) = 3/10` then P(B/A) is equal to

Options

A. `1/5`
B. `3/10`
C. `1/2`
D. `3/5`

Answer

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

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

### Step 1: Write down the given probabilities
- \( P(A) = \frac{1}{2} \)
- \( P(B) = \frac{3}{5} \)
- \( P(A \cap B) = \frac{3}{10} \)

### Step 2: Substitute the values into the formula
Now we substitute the values we have into the formula for conditional probability:

\[ P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{3}{10}}{\frac{1}{2}} \]

### Step 3: Simplify the expression
To simplify the fraction, we can multiply by the reciprocal of the denominator:

\[ P(B|A) = \frac{3}{10} \times \frac{2}{1} = \frac{3 \times 2}{10 \times 1} = \frac{6}{10} \]

### Step 4: Reduce the fraction
Now, we can reduce \( \frac{6}{10} \):

\[ P(B|A) = \frac{6 \div 2}{10 \div 2} = \frac{3}{5} \]

### Final Answer
Thus, the probability \( P(B|A) \) is:

\[ P(B|A) = \frac{3}{5} \]