A and B are two events such that P(A)= 0.8, P(B) = 0.6 and P `(Ann B) = 0.5,` then the value of P(A/B) is

Options

A. `(5)/(6)`
B. `(5)/(8)`
C. `(9)/(10)`
D. `(6)/(5)`

Answer

To find the value of \( P(A|B) \), which is the conditional probability of event A given event B, we can use the formula:

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

Where:
- \( P(A \cap B) \) is the probability of both A and B occurring.
- \( P(B) \) is the probability of event B.

Given:
- \( P(A) = 0.8 \)
- \( P(B) = 0.6 \)
- \( P(A \cap B) = 0.5 \)

Now, we can substitute the values into the formula.

### Step 1: Substitute the values into the formula
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.5}{0.6} \]

### Step 2: Calculate the fraction
To simplify \( \frac{0.5}{0.6} \):
\[ P(A|B) = \frac{0.5 \div 0.1}{0.6 \div 0.1} = \frac{5}{6} \]

### Step 3: Final answer
Thus, the value of \( P(A|B) \) is:
\[ P(A|B) = \frac{5}{6} \approx 0.8333 \]