To find \( P(A|B) \), we can use the formula:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
First, we need to find \( P(A \cap B) \). We can use the inclusion-exclusion principle for probabilities, which states:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
We know:
\[ P(A) = 0.27, \quad P(B) = 0.35, \quad P(A \cup B) = 0.38 \]
Plugging the known values into the formula gives:
\[ 0.38 = 0.27 + 0.35 - P(A \cap B) \]
Now, let's combine the values to solve for \( P(A \cap B) \):
\[ 0.38 = 0.62 - P(A \cap B) \]
Rearranging gives:
\[ P(A \cap B) = 0.62 - 0.38 = 0.24 \]
Now that we have \( P(A \cap B) \), we can calculate \( P(A|B) \):
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.24}{0.35} \]
Calculating the fraction yields:
\[ P(A|B) = \frac{0.24}{0.35} \approx 0.6857 \]
Rounding to the nearest tenth, we get:
\[ P(A|B) \approx 0.7 \]
Thus, the final answer is:
\[ \boxed{0.7} \]