The probabilities of events E, F, and EnF are given below. Find (a) P(EIF), (b) P(FIE), (c) P (EIF'), and (d) P (FIE') P(E)=0.7, P(F) = 0.3, P(EnF) = 0.1 a. P(EIF) = (Type an integer or decimal rounded to two decimal places as needed.) b. P(FIE) = (Type an integer or decimal rounded to two decimal places as needed.) C. P (EIF') = (Type an integer or decimal rounded to two decimal places as needed.) d. P (FIE') = (Type an integer or decimal rounded to two decimal places as needed.) ...
The probabilities of events E, F, and EnF are given below. Find (a) P(EIF), (b) P(FIE), (c) P (EIF'), and (d) P (FIE') P(E)=0.7, P(F) = 0.3, P(EnF) = 0.1 a. P(EIF) = (Type an integer or decimal rounded to two decimal places as needed.) b. P(FIE) = (Type an integer or decimal rounded to two decimal places as needed.) C. P (EIF') = (Type an integer or decimal rounded to two decimal places as needed.) d. P (FIE') = (Type an integer or decimal rounded to two decimal places as needed.) ...
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Probability Concepts and Calculation**
In this exercise, we are exploring various probabilities related to events E and F. Given below are the probabilities of events E, F, and their intersection \(E \cap F\). Using this information, we aim to find the probabilities for (a) \( P(E|F) \), (b) \( P(F|E) \), (c) \( P(E|F') \), and (d) \( P(F|E') \).
**Given:**
- \( P(E) = 0.7 \)
- \( P(F) = 0.3 \)
- \( P(E \cap F) = 0.1 \)
**Tasks:**
1. **a. \( P(E|F) \)**
- This is the conditional probability of event E occurring given that event F has occurred.
- Calculate \( P(E|F) \) using the formula:
\[
P(E|F) = \frac{P(E \cap F)}{P(F)}
\]
- **Solution:**
\[
P(E|F) = \frac{0.1}{0.3} \approx 0.33
\]
- Complete the answer with a rounded value to two decimal places as needed.
2. **b. \( P(F|E) \)**
- This is the conditional probability of event F occurring given that event E has occurred.
- Calculate \( P(F|E) \) using the formula:
\[
P(F|E) = \frac{P(E \cap F)}{P(E)}
\]
- **Solution:**
\[
P(F|E) = \frac{0.1}{0.7} \approx 0.14
\]
- Complete the answer with a rounded value to two decimal places as needed.
3. **c. \( P(E|F') \)**
- This is the conditional probability of event E occurring given that event F has not occurred.
- Calculate \( P(E|F') \) using the formula:
\[
P(E|F') = \frac{P(E) - P(E \cap F)}{1 - P(F)}
\]
- **Solution:**
\[
P(E|F') = \frac{0.7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff138e77-4b21-4b3f-a581-600ea0faba85%2F153ab824-277d-48b4-a535-d1001d772488%2F1h2q45g_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability Concepts and Calculation**
In this exercise, we are exploring various probabilities related to events E and F. Given below are the probabilities of events E, F, and their intersection \(E \cap F\). Using this information, we aim to find the probabilities for (a) \( P(E|F) \), (b) \( P(F|E) \), (c) \( P(E|F') \), and (d) \( P(F|E') \).
**Given:**
- \( P(E) = 0.7 \)
- \( P(F) = 0.3 \)
- \( P(E \cap F) = 0.1 \)
**Tasks:**
1. **a. \( P(E|F) \)**
- This is the conditional probability of event E occurring given that event F has occurred.
- Calculate \( P(E|F) \) using the formula:
\[
P(E|F) = \frac{P(E \cap F)}{P(F)}
\]
- **Solution:**
\[
P(E|F) = \frac{0.1}{0.3} \approx 0.33
\]
- Complete the answer with a rounded value to two decimal places as needed.
2. **b. \( P(F|E) \)**
- This is the conditional probability of event F occurring given that event E has occurred.
- Calculate \( P(F|E) \) using the formula:
\[
P(F|E) = \frac{P(E \cap F)}{P(E)}
\]
- **Solution:**
\[
P(F|E) = \frac{0.1}{0.7} \approx 0.14
\]
- Complete the answer with a rounded value to two decimal places as needed.
3. **c. \( P(E|F') \)**
- This is the conditional probability of event E occurring given that event F has not occurred.
- Calculate \( P(E|F') \) using the formula:
\[
P(E|F') = \frac{P(E) - P(E \cap F)}{1 - P(F)}
\]
- **Solution:**
\[
P(E|F') = \frac{0.7
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