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`

Answer

To solve the problem, we need to find \( P(B|A) \) using the formula for conditional probability:

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

**Step 1: Identify the given probabilities.**
- We have \( P(A) = \frac{4}{5} \)
- We have \( P(A \cap B) = \frac{7}{10} \)

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

**Step 4: Perform the multiplication.**
\[ P(B|A) = \frac{7 \times 5}{10 \times 4} = \frac{35}{40} \]

**Step 5: Simplify the fraction.**
\[ P(B|A) = \frac{35 \div 5}{40 \div 5} = \frac{7}{8} \]

Thus, the final answer is:
\[ P(B|A) = \frac{7}{8} \]