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 solve the problem step by step, we will use the given probabilities and the formula for conditional probability.

### Step 1: Write down the given probabilities.
We are given:
- \( P(A) = \frac{4}{5} \)
- \( P(A \cap B) = \frac{7}{10} \)

### Step 2: Recall the formula for conditional probability.
The formula for conditional probability \( P(B|A) \) is given by:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} \]

### Step 3: Substitute the known values into the formula.
Now, we can substitute the values we have into the formula:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{10}}{\frac{4}{5}} \]

### Step 4: Simplify the expression.
To simplify the fraction, we multiply by the reciprocal of the denominator:
\[ P(B|A) = \frac{7}{10} \times \frac{5}{4} \]

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

### Step 6: Simplify the fraction.
Now, we simplify \( \frac{35}{40} \):
\[ P(B|A) = \frac{35 \div 5}{40 \div 5} = \frac{7}{8} \]

### Step 7: Conclusion.
Thus, the value of \( P(B|A) \) is:
\[ P(B|A) = \frac{7}{8} \]

### Final Answer:
The answer is \( \frac{7}{8} \).

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