If `P(A ) =4/5 and P( A cap B) =7/10` then P(B/A) is equal to

Options

A. `1/10`
B. `1/8`
C. `7/8`
D. `17/20`

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: Identify the given values
We have:
- \( P(A) = \frac{4}{5} \)
- \( P(A \cap B) = \frac{7}{10} \)

### Step 2: Substitute the values into the formula
Now, substitute the values into the conditional probability formula:

\[ P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{10}}{\frac{4}{5}} \]

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

\[ P(B|A) = \frac{7}{10} \times \frac{5}{4} \]

### Step 4: Perform the multiplication
Now, perform the multiplication:

\[ P(B|A) = \frac{7 \times 5}{10 \times 4} = \frac{35}{40} \]

### Step 5: Simplify the result
Now, simplify \( \frac{35}{40} \):

\[ P(B|A) = \frac{7}{8} \]

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

\[ \boxed{\frac{7}{8}} \]