For two dependent events A and B. it is given that P(A) = 0.2 and P(B) = 0.5. If `A sube B`, then the values of conditional probabilities P (A|B) and P(B|A) are respectively:

Options

A. `(2)/(5), (3)/(5)`
B. `(2)/(5), 1`
C. `1, (2)/(5)`
D. Information is insufficient

Answer

To solve the problem, we need to find the conditional probabilities \( P(A|B) \) and \( P(B|A) \) given the probabilities \( P(A) = 0.2 \) and \( P(B) = 0.5 \), and the information that event A is a subset of event B (denoted as \( A \subseteq B \)).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
Since \( A \subseteq B \), this implies that every outcome in A is also in B. Therefore, the intersection of A and B is equal to A itself:
\[ P(A \cap B) = P(A) \]

2. **Finding \( P(A|B) \)**:
The formula for conditional probability is:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
Substituting the values we have:
\[ P(A|B) = \frac{P(A)}{P(B)} = \frac{0.2}{0.5} \]
Simplifying this gives:
\[ P(A|B) = 0.4 \]

3. **Finding \( P(B|A) \)**:
Similarly, we can find \( P(B|A) \) using the conditional probability formula:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} \]
Again, substituting the values:
\[ P(B|A) = \frac{P(A)}{P(A)} = \frac{0.2}{0.2} \]
This simplifies to:
\[ P(B|A) = 1 \]

### Final Answers:
Thus, the values of the conditional probabilities are:
- \( P(A|B) = 0.4 \)
- \( P(B|A) = 1 \)