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The probabilities of events A, B, and An B are given. Find (a) P(A U B), (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) = 0.69 (Simplify your answer.) (b) The odds in favor of A are 27 73. (Simplify your answer. Type whole numbers.) The odds against A are 73:27 (Simplify your answer. Type whole numbers.) (c) The odds in favor of B are 3:2. (Simplify your answer. Type whole numbers.) The odds against B are 2:3. (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 (Ci 10:0

The probabilities of events A, B, and An B are given. Find (a) P(A U B), (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) = 0.69 (Simplify your answer.) (b) The odds in favor of A are 27 73. (Simplify your answer. Type whole numbers.) The odds against A are 73:27 (Simplify your answer. Type whole numbers.) (c) The odds in favor of B are 3:2. (Simplify your answer. Type whole numbers.) The odds against B are 2:3. (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 (Ci 10:0

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Part D

**Title: Understanding Probability and Odds in Events** --- **Introduction to Probability and Odds** The probabilities of events A, B, and \(A \cap B\) are given. We will find (a) \(P(A \cup B)\), (b) the odds in favor of A and the odds against A, (c) the odds in favor of B and the odds against B, and (d) the odds in favor of and against \(A \cap B\). Given: \[ P(A) = 0.27, \, P(B) = 0.6, \, P(A \cap B) = 0.18 \] --- **(a) Finding \(P(A \cup B)\)** \[ P(A \cup B) = 0.69 \] (Simplify your answer.) --- **(b) The Odds in Favor and Against Event A** - The odds in favor of A are \( \frac{27}{73} \). (Simplify your answer. Type whole numbers.) - The odds against A are \( \frac{73}{27} \). (Simplify your answer. Type whole numbers.) --- **(c) The Odds in Favor and Against Event B** - The odds in favor of B are \( 3 \) : \( 2 \). (Simplify your answer. Type whole numbers.) - The odds against B are \( 2 \) : \( 3 \). (Simplify your answer. Type whole numbers.) --- **(d) The Odds in Favor and Against Event \(A \cap B\)** - The odds in favor of \(A \cap B\) are \(\boxed{?} \) : \(\boxed{?}\). (Simplify your answer. Type whole numbers.) - The odds against \(A \cap B\) are \(\boxed{?} \) : \(\boxed{?}\). (Simplify your answer. Type whole numbers.) --- **Explanation of Diagrams or Graphs** This exercise does not include any graphs or diagrams. The problems involve calculating probabilities and odds based on given probabilities of events A, B, and their intersection. --- **Conclusion** Understanding the relationships between different events, their probabilities, and their odds is a crucial aspect of probability theory. The exercises above guide you through the process of calculating these values step-by-step.
Transcribed Image Text:**Title: Understanding Probability and Odds in Events** --- **Introduction to Probability and Odds** The probabilities of events A, B, and \(A \cap B\) are given. We will find (a) \(P(A \cup B)\), (b) the odds in favor of A and the odds against A, (c) the odds in favor of B and the odds against B, and (d) the odds in favor of and against \(A \cap B\). Given: \[ P(A) = 0.27, \, P(B) = 0.6, \, P(A \cap B) = 0.18 \] --- **(a) Finding \(P(A \cup B)\)** \[ P(A \cup B) = 0.69 \] (Simplify your answer.) --- **(b) The Odds in Favor and Against Event A** - The odds in favor of A are \( \frac{27}{73} \). (Simplify your answer. Type whole numbers.) - The odds against A are \( \frac{73}{27} \). (Simplify your answer. Type whole numbers.) --- **(c) The Odds in Favor and Against Event B** - The odds in favor of B are \( 3 \) : \( 2 \). (Simplify your answer. Type whole numbers.) - The odds against B are \( 2 \) : \( 3 \). (Simplify your answer. Type whole numbers.) --- **(d) The Odds in Favor and Against Event \(A \cap B\)** - The odds in favor of \(A \cap B\) are \(\boxed{?} \) : \(\boxed{?}\). (Simplify your answer. Type whole numbers.) - The odds against \(A \cap B\) are \(\boxed{?} \) : \(\boxed{?}\). (Simplify your answer. Type whole numbers.) --- **Explanation of Diagrams or Graphs** This exercise does not include any graphs or diagrams. The problems involve calculating probabilities and odds based on given probabilities of events A, B, and their intersection. --- **Conclusion** Understanding the relationships between different events, their probabilities, and their odds is a crucial aspect of probability theory. The exercises above guide you through the process of calculating these values step-by-step.
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