### Problem Statement:If \( P(A) = 0.3 \) and \( P(B) = 0.2 \), what is \( P(A \text{ and } B) \)?#### Explanation:To solve this, we need additional information about the relationship between events \( A \) and \( B \):1. **Independent Events:** If \( A \) and \( B \) are independent events, then the probability of both \( A \) and \( B \) occurring is the product of their individual probabilities.\[ P(A \text{ and } B) = P(A) \times P(B) \]Given \( P(A) = 0.3 \) and \( P(B) = 0.2 \),\[ P(A \text{ and } B) = 0.3 \times 0.2 = 0.06 \]2. **Mutually Exclusive Events:** If \( A \) and \( B \) are mutually exclusive events, then \( P(A \text{ and } B) = 0 \), because the events cannot occur simultaneously.\[ P(A \text{ and } B) = 0 \]3. **General Case:** If no specific relationship is given, we cannot determine \( P(A \text{ and } B) \) solely based on the given information. Additional data on the dependency or overlap between the events is required.### Conclusion:Without specific information about whether the events \( A \) and \( B \) are independent or mutually exclusive, the exact value of \( P(A \text{ and } B) \) cannot be determined beyond the individual probabilities provided. However, under the assumption of independence, \( P(A \text{ and } B) = 0.06 \).

Name: ### Problem Statement:If \( P(A) = 0.3 \) and \( P(B) = 0.2 \), what
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: ### Problem Statement:If \( P(A) = 0.3 \) and \( P(B) = 0.2 \), what is \( P(A \text{ and } B) \)?#### Explanation:To solve this, we need additional information about the relationship between events \( A \) and \( B \):1. **Independent Events:** If