If `P(AcapB)=7/10 and P(B)=17/20`,then P(A/B) equals to

Options

A. `1//4`
B. `1//3`
C. `5//12`
D. `7//12`

Answer

To solve the problem, we need to find \( P(A|B) \) using the given probabilities \( P(A \cap B) \) and \( P(B) \).

### Step-by-Step Solution:

1. **Identify the given values:**
- \( P(A \cap B) = \frac{7}{10} \)
- \( P(B) = \frac{17}{20} \)

2. **Use the formula for conditional probability:**
The formula for conditional probability is:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

3. **Substitute the given values into the formula:**
\[ P(A|B) = \frac{\frac{7}{10}}{\frac{17}{20}} \]

4. **Simplify the expression:**
To divide by a fraction, we multiply by its reciprocal:
\[ P(A|B) = \frac{7}{10} \times \frac{20}{17} \]

5. **Perform the multiplication:**
- Multiply the numerators: \( 7 \times 20 = 140 \)
- Multiply the denominators: \( 10 \times 17 = 170 \)
\[ P(A|B) = \frac{140}{170} \]

6. **Simplify the fraction:**
Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 10:
\[ P(A|B) = \frac{14}{17} \]

### Final Answer:
Thus, \( P(A|B) = \frac{14}{17} \).

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