4. | Basic Computation: Addition Rule Given P(A) = 0.7 and P(B) = 0.4: (a) Can events A and B be mutually exclusive? Explain. (b) If P(A and B) = 0.2, compute P(A or B). 5. | Basic Computation: Multiplication Rule Given P(A) = 0.2 and P(B) = 0.4: (a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.1, compute P(A and B). 6. Basic Computation: Multiplication Rule Given P(A) = 0.7 and P(B) = 0.8: (a) If A and B, are independent events, compute P(A and B). (b) If P(BIA) = 0.9, compute P(A and B). 7. | Basic Computations: Rules of Probability Given P(A) = 0.2. P(B) = 0.5.
4. | Basic Computation: Addition Rule Given P(A) = 0.7 and P(B) = 0.4: (a) Can events A and B be mutually exclusive? Explain. (b) If P(A and B) = 0.2, compute P(A or B). 5. | Basic Computation: Multiplication Rule Given P(A) = 0.2 and P(B) = 0.4: (a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.1, compute P(A and B). 6. Basic Computation: Multiplication Rule Given P(A) = 0.7 and P(B) = 0.8: (a) If A and B, are independent events, compute P(A and B). (b) If P(BIA) = 0.9, compute P(A and B). 7. | Basic Computations: Rules of Probability Given P(A) = 0.2. P(B) = 0.5.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 36E
Related questions
Question
Please please answer number 4 and 6. Make sure to show work! Thank you!
Transcribed Image Text:### Basic Computation: Probability Rules
#### 4. Basic Computation: Addition Rule
Given \(P(A) = 0.7\) and \(P(B) = 0.4\):
- (a) Can events \(A\) and \(B\) be mutually exclusive? Explain.
- (b) If \(P(A \text{ and } B) = 0.2\), compute \(P(A \text{ or } B)\).
#### 5. Basic Computation: Multiplication Rule
Given \(P(A) = 0.2\) and \(P(B) = 0.4\):
- (a) If \(A\) and \(B\) are independent events, compute \(P(A \text{ and } B)\).
- (b) If \(P(A | B) = 0.1\), compute \(P(A \text{ and } B)\).
#### 6. Basic Computation: Multiplication Rule
Given \(P(A) = 0.7\) and \(P(B) = 0.8\):
- (a) If \(A\) and \(B\) are independent events, compute \(P(A \text{ and } B)\).
- (b) If \(P(B | A) = 0.9\), compute \(P(A \text{ and } B)\).
#### 7. Basic Computations: Rules of Probability
Given \(P(A) = 0.2\), \(P(B) = 0.5\), \(P(A | B) = 0.3\):
- (a) Compute \(P(A \text{ and } B)\).
- (b) Compute \(P(A \text{ or } B)\).
#### 8. Basic Computation: Rules of Probability
Given \(P(A^\text{c}) = 0.8\), \(P(B) = 0.3\), \(P(B | A) = 0.2\):
- (a) Compute \(P(A \text{ and } B)\).
- (b) Compute \(P(A \text{ or } B)\).
### Explanation of Probability Calculations
- **Addition Rule**: For any two events \(A\) and \(B\):
\[
P(A \text{ or } B) = P(A) + P(B
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