If `P(E)=(7)/(13),P(F)=(9)/(13)` and `P(E nn F)=(4)/(13)`, then `P(E//F)`__________.

Options

A. `(4)/(7)`
B. `(2)/(9)`
C. `(4)/(9)`
D. `(2)/(7)`

Answer

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

\[ P(E|F) = \frac{P(E \cap F)}{P(F)} \]

### Step 1: Identify the given probabilities
We are given:
- \( P(E) = \frac{7}{13} \)
- \( P(F) = \frac{9}{13} \)
- \( P(E \cap F) = \frac{4}{13} \)

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the formula for conditional probability:

\[ P(E|F) = \frac{P(E \cap F)}{P(F)} = \frac{\frac{4}{13}}{\frac{9}{13}} \]

### Step 3: Simplify the expression
To simplify the fraction, we can multiply by the reciprocal of the denominator:

\[ P(E|F) = \frac{4}{13} \times \frac{13}{9} \]

### Step 4: Cancel out the common terms
The \( 13 \) in the numerator and the denominator cancels out:

\[ P(E|F) = \frac{4}{9} \]

### Final Answer
Thus, the probability \( P(E|F) \) is:

\[ \boxed{\frac{4}{9}} \]