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Answer:
To find \( P(A \text{ and } B) \), we use the definition of conditional probability, which is given by:
\[ P(A|B) = \frac{P(A \text{ and } B)}{P(B)} \]
Given:
- \( P(A|B) = 0.85 \)
- \( P(B) = 0.35 \)
Rearranging the formula to solve for \( P(A \text{ and } B) \):
\[ P(A \text{ and } B) = P(A|B) \times P(B) \]
Substitute the given values:
\[ P(A \text{ and } B) = 0.85 \times 0.35 \]
Calculate the result:
\[ P(A \text{ and } B) = 0.2975 \]
So, \( P(A \text{ and } B) = 0.2975 \).