In a class 45% students read English, 30% read French and 20% read both English and French. One student is selected at random find the probability that he reads French, if it is known that he reads English.

Options

A. `4/9`
B. `5/9`
C. `2/9`
D. `1/9`

Answer

To solve the problem, we need to find the probability that a student reads French given that they read English. This can be expressed using conditional probability.

### Step-by-Step Solution:

1. **Define the Events:**
- Let \( E \) be the event that a student reads English.
- Let \( F \) be the event that a student reads French.

2. **Given Information:**
- \( P(E) = 0.45 \) (45% of students read English)
- \( P(F) = 0.30 \) (30% of students read French)
- \( P(E \cap F) = 0.20 \) (20% of students read both English and French)

3. **Use the Conditional Probability Formula:**
The conditional probability \( P(F | E) \) is given by the formula:
\[ P(F | E) = \frac{P(E \cap F)}{P(E)} \]

4. **Substitute the Values:**
Substitute the known probabilities into the formula:
\[ P(F | E) = \frac{P(E \cap F)}{P(E)} = \frac{0.20}{0.45} \]

5. **Calculate the Probability:**
To simplify \( \frac{0.20}{0.45} \):
\[ P(F | E) = \frac{20}{45} = \frac{4}{9} \]

6. **Final Answer:**
The probability that a student reads French given that they read English is \( \frac{4}{9} \).