If P(E) = 0.2, P(F) = 0.3, and E and F are independent events, find P(E and F). 1) 0.06 2) 0.08 3) 0.1 4) 0.12
If P(E) = 0.2, P(F) = 0.3, and E and F are independent events, find P(E and F). 1) 0.06 2) 0.08 3) 0.1 4) 0.12
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.3: Using Data Displays
Problem 2C
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![**Problem Statement:**
Given:
- \( P(E) = 0.2 \)
- \( P(F) = 0.3 \)
- E and F are independent events
Find \( P(E \text{ and } F) \).
**Options:**
1. \( 0.06 \)
2. \( 0.08 \)
3. \( 0.1 \)
4. \( 0.12 \)
5. \( 0.5 \)
6. \( 0.9 \)
7. \( 0 \)
8. \( 1 \)
**Solution:**
To find the probability of both events E and F occurring, denoted \( P(E \text{ and } F) \), we use the fact that the events are independent. For independent events, the probability of both occurring is the product of their individual probabilities:
\[
P(E \text{ and } F) = P(E) \times P(F)
\]
Given:
\[
P(E) = 0.2 \quad \text{and} \quad P(F) = 0.3
\]
Therefore:
\[
P(E \text{ and } F) = 0.2 \times 0.3 = 0.06
\]
**Answer:**
The correct option is:
1. \( 0.06 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a8ca984-2571-47a4-a8f9-ecaefc8de4f3%2Fccc95424-f4fc-43dd-bf9d-3ae9689e962e%2Fy6f6wyh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given:
- \( P(E) = 0.2 \)
- \( P(F) = 0.3 \)
- E and F are independent events
Find \( P(E \text{ and } F) \).
**Options:**
1. \( 0.06 \)
2. \( 0.08 \)
3. \( 0.1 \)
4. \( 0.12 \)
5. \( 0.5 \)
6. \( 0.9 \)
7. \( 0 \)
8. \( 1 \)
**Solution:**
To find the probability of both events E and F occurring, denoted \( P(E \text{ and } F) \), we use the fact that the events are independent. For independent events, the probability of both occurring is the product of their individual probabilities:
\[
P(E \text{ and } F) = P(E) \times P(F)
\]
Given:
\[
P(E) = 0.2 \quad \text{and} \quad P(F) = 0.3
\]
Therefore:
\[
P(E \text{ and } F) = 0.2 \times 0.3 = 0.06
\]
**Answer:**
The correct option is:
1. \( 0.06 \)
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