Use the Test for Independence to determine if events A and B are independent. 6 6 P(A) = 7, P(B) = 7, P(An B) = - 49
Use the Test for Independence to determine if events A and B are independent. 6 6 P(A) = 7, P(B) = 7, P(An B) = - 49
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Test for Independence of Events
To determine if events A and B are independent, we will use the given probabilities:
\[ P(A) = \frac{6}{7}, \quad P(B) = \frac{1}{7}, \quad P(A \cap B) = \frac{6}{49} \]
We can test for independence using the following principle:
\[ P(A \cap B) = P(A) \times P(B) \]
**Step-by-Step Solution:**
1. **Calculate \( P(A) \times P(B) \):**
\[ P(A) \times P(B) = \frac{6}{7} \times \frac{1}{7} = \frac{6}{49} \]
2. **Compare \( P(A \cap B) \) with \( P(A) \times P(B) \):**
Since \( P(A \cap B) = \frac{6}{49} \) and \( P(A) \times P(B) = \frac{6}{49} \), we can conclude that the events are independent because the two values are equal.
**Multiple Choice Question:**
_Select the correct choice below and fill in any answer box(es) to complete your choice. (Type an integer or a simplified fraction.)_
1. \(\circ \quad \text{A. Events A and B are independent because } P(A \cap B) = \frac{6}{49} \text{ and } P(A) \cdot P(B) = \boxed{\frac{6}{49}}. \)
2. \(\circ \quad \text{B. Events A and B are not independent because } P(A \cup B) = \boxed{\phantom{\frac{ }}{}} \text{ and } P(A) + P(B) - P(A \cap B) = \boxed{\phantom{\frac{ }}{}}. \)
3. \(\circ \quad \text{C. Events A and B are independent because } P(A \cup B) = \boxed{\phantom{\frac{ }}{}} \text{ and } P(A) + P(B) - P(A \cap B) = \boxed{\phantom{\frac{ }}{}}. \)
4. \(\circ \quad \text{D. Events A and B are not independent because } P(A \cap B](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b1d7e88-5924-4190-9ef7-53bc83ebfef1%2F5a6e804b-e4c1-4905-b1aa-ad0bd65056bd%2Fp4a6ws6_processed.png&w=3840&q=75)
Transcribed Image Text:### Test for Independence of Events
To determine if events A and B are independent, we will use the given probabilities:
\[ P(A) = \frac{6}{7}, \quad P(B) = \frac{1}{7}, \quad P(A \cap B) = \frac{6}{49} \]
We can test for independence using the following principle:
\[ P(A \cap B) = P(A) \times P(B) \]
**Step-by-Step Solution:**
1. **Calculate \( P(A) \times P(B) \):**
\[ P(A) \times P(B) = \frac{6}{7} \times \frac{1}{7} = \frac{6}{49} \]
2. **Compare \( P(A \cap B) \) with \( P(A) \times P(B) \):**
Since \( P(A \cap B) = \frac{6}{49} \) and \( P(A) \times P(B) = \frac{6}{49} \), we can conclude that the events are independent because the two values are equal.
**Multiple Choice Question:**
_Select the correct choice below and fill in any answer box(es) to complete your choice. (Type an integer or a simplified fraction.)_
1. \(\circ \quad \text{A. Events A and B are independent because } P(A \cap B) = \frac{6}{49} \text{ and } P(A) \cdot P(B) = \boxed{\frac{6}{49}}. \)
2. \(\circ \quad \text{B. Events A and B are not independent because } P(A \cup B) = \boxed{\phantom{\frac{ }}{}} \text{ and } P(A) + P(B) - P(A \cap B) = \boxed{\phantom{\frac{ }}{}}. \)
3. \(\circ \quad \text{C. Events A and B are independent because } P(A \cup B) = \boxed{\phantom{\frac{ }}{}} \text{ and } P(A) + P(B) - P(A \cap B) = \boxed{\phantom{\frac{ }}{}}. \)
4. \(\circ \quad \text{D. Events A and B are not independent because } P(A \cap B
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