The probabilities of events A, B, and AnB are given. Find (a) P(A UB), (b) the odds in favor of and the odds against A, (c) the odds in favor of and the odds against B, and (d) the odds in favor of and against An B. P(A) = 0.27, P(B) = 0.6, P(An B) = 0.18 (a) P(A U B)= (Simplify your answer.) (b) The odds in favor of A are: (Simplify your answer. Type whole numbers.) The odds against A are (Simplify your answer. Type whole numbers.) (c) The odds in favor of B are: (Simplify your answer. Type whole numbers.) The odds against B are (Simplify your answer. Type whole numbers.) (d) The odds in favor of An B are: (Simplify your answer. Type whole numbers.) The odds against An B are: (Simplify your answer. Type whole numbers.)
The probabilities of events A, B, and AnB are given. Find (a) P(A UB), (b) the odds in favor of and the odds against A, (c) the odds in favor of and the odds against B, and (d) the odds in favor of and against An B. P(A) = 0.27, P(B) = 0.6, P(An B) = 0.18 (a) P(A U B)= (Simplify your answer.) (b) The odds in favor of A are: (Simplify your answer. Type whole numbers.) The odds against A are (Simplify your answer. Type whole numbers.) (c) The odds in favor of B are: (Simplify your answer. Type whole numbers.) The odds against B are (Simplify your answer. Type whole numbers.) (d) The odds in favor of An B are: (Simplify your answer. Type whole numbers.) The odds against An B are: (Simplify your answer. Type whole numbers.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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![### Calculating Probabilities and Odds in a Given Scenario
The probabilities of events \( A \), \( B \), and \( A \cap B \) are given. Find the following:
1. **Union of Events**: \( P(A \cup B) \)
2. **Odds Calculation**:
- Odds in favor of \( A \)
- Odds against \( A \)
- Odds in favor of \( B \)
- Odds against \( B \)
- Odds in favor of \( A \cap B \)
- Odds against \( A \cap B \)
Given probabilities:
\[ P(A) = 0.27, \ P(B) = 0.6, \ P(A \cap B) = 0.18 \]
#### Problem Statements
(a) Find \( P(A \cup B) \):
\[ P(A \cup B) = \ \text{(Simplify your answer.)} \]
---
(b) The odds in favor of \( A \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
The odds against \( A \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
---
(c) The odds in favor of \( B \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
The odds against \( B \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
---
(d) The odds in favor of \( A \cap B \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
The odds against \( A \cap B \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
---
This problem involves understanding the basics of probability and odds. The formulas necessary for these calculations are as follows:
- To find the union of two events:
\[ P(A \cup B) = P(A) + P](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b1d7e88-5924-4190-9ef7-53bc83ebfef1%2F5506086c-d00a-45ae-b515-992de2efe9f9%2F0xmovm_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating Probabilities and Odds in a Given Scenario
The probabilities of events \( A \), \( B \), and \( A \cap B \) are given. Find the following:
1. **Union of Events**: \( P(A \cup B) \)
2. **Odds Calculation**:
- Odds in favor of \( A \)
- Odds against \( A \)
- Odds in favor of \( B \)
- Odds against \( B \)
- Odds in favor of \( A \cap B \)
- Odds against \( A \cap B \)
Given probabilities:
\[ P(A) = 0.27, \ P(B) = 0.6, \ P(A \cap B) = 0.18 \]
#### Problem Statements
(a) Find \( P(A \cup B) \):
\[ P(A \cup B) = \ \text{(Simplify your answer.)} \]
---
(b) The odds in favor of \( A \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
The odds against \( A \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
---
(c) The odds in favor of \( B \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
The odds against \( B \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
---
(d) The odds in favor of \( A \cap B \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
The odds against \( A \cap B \) are \( \dfrac{ \ \ldots\ }{ \ \ldots\ } \):
(Simplify your answer. Type whole numbers.)
---
This problem involves understanding the basics of probability and odds. The formulas necessary for these calculations are as follows:
- To find the union of two events:
\[ P(A \cup B) = P(A) + P
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