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

Options

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

Explanation

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

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

Given:
- \( P(A) = \frac{4}{5} \)
- \( P(A \cap B) = \frac{7}{10} \)

Now, we can substitute the given values into the formula.

### Step 1: Substitute the values into the formula
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{10}}{\frac{4}{5}} \]

### Step 2: Simplify the fraction
To divide by a fraction, we multiply by its reciprocal:
\[ P(B|A) = \frac{7}{10} \times \frac{5}{4} \]

### Step 3: Perform the multiplication
Now, we multiply the numerators and the denominators:
\[ P(B|A) = \frac{7 \times 5}{10 \times 4} = \frac{35}{40} \]

### Step 4: Simplify the result
Now, we simplify \( \frac{35}{40} \):
\[ P(B|A) = \frac{35 \div 5}{40 \div 5} = \frac{7}{8} \]

### Final Answer
Thus, \( P(B|A) = \frac{7}{8} \).

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