If 4P(A) = 6P(B) = `10P(AcapB)=1`, then `P(B/A)`

Options

A. `2/5`
B. `3/5`
C. `7/10`
D. `19/60`

Answer

To solve the problem, we need to find \( P(B|A) \) given the equations:

1. \( 4P(A) = 6P(B) = 10P(A \cap B) = 1 \)

### Step 1: Express \( P(A) \), \( P(B) \), and \( P(A \cap B) \)

From the equation \( 4P(A) = 1 \):
\[ P(A) = \frac{1}{4} \]

From the equation \( 10P(A \cap B) = 1 \):
\[ P(A \cap B) = \frac{1}{10} \]

Now we need to find \( P(B) \). We can use the equation \( 6P(B) = 1 \):
\[ P(B) = \frac{1}{6} \]

### Step 2: Use the formula for conditional probability

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

### Step 3: Substitute the values we found

Now substituting the values we calculated:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{1}{10}}{\frac{1}{4}} \]

### Step 4: Simplify the expression

To simplify:
\[ P(B|A) = \frac{1}{10} \times \frac{4}{1} = \frac{4}{10} = \frac{2}{5} \]

### Conclusion

Thus, the value of \( P(B|A) \) is:
\[ \boxed{\frac{2}{5}} \]