Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 4 - Probability and Counting Rules - 4-1 Sample Spaces and Probability - Extending the Concepts - Page 201: 47

Answer

a. odds in favor =$\frac{1}{5}$ odds against =$\frac{5}{1}$ b. odds in favor =$\frac{1}{1}$ odds against =$\frac{1}{1}$ c. odds in favor =$\frac{1}{3}$ odds against =$\frac{3}{1}$ d. odds in favor =$\frac{1}{1}$ odds against =$\frac{1}{1}$ e. odds in favor =$\frac{1}{12}$ odds against =$\frac{12}{1}$ f. odds in favor =$\frac{1}{3}$ odds against =$\frac{3}{1}$ g. odds in favor =$\frac{1}{1}$ odds against =$\frac{1}{1}$

Work Step by Step

a. Rolling a die and getting a 2, $p_{1}=1/6, p_{2}=1-p_{1}=5/6$ odds in favor =$\frac{1/6}{1-1/6}=\frac{1}{5}$ odds against =$\frac{5/6}{1-1/6}=\frac{5}{1}$ b. Rolling a die and getting an even number, $p_{1}=3/6=1/2=p_{2}$ odds in favor =$\frac{1/2}{1-1/2}=\frac{1}{1}$ odds against =$\frac{1/2}{1-1/2}=\frac{1}{1}$ c. Drawing a card from a deck and getting a spade, $p_{1}=13/52=1/4, p_{2}=3/4$ odds in favor =$\frac{1/4}{1-1/4}=\frac{1}{3}$ odds against =$\frac{3/4}{1-3/4}=\frac{3}{1}$ d. Drawing a card and getting a red card, $p_{1}=26/52=1/2= p_{2}$ odds in favor =$\frac{1/2}{1-1/2}=\frac{1}{1}$ odds against =$\frac{1/2}{1-1/2}=\frac{1}{1}$ e. Drawing a card and getting a queen, $p_{1}=4/52=1/13, p_{2}=12/13$ odds in favor =$\frac{1/13}{1-1/13}=\frac{1}{12}$ odds against =$\frac{12/13}{1-12/13}=\frac{12}{1}$ f. Tossing two coins and getting two tails, $p_{1}=1/4, p_{2}=3/4$ odds in favor =$\frac{1/4}{1-1/4}=\frac{1}{3}$ odds against =$\frac{3/4}{1-3/4}=\frac{3}{1}$ g. Tossing two coins and getting exactly one tail, $p_{1}=1/2, p_{2}=1/2$ odds in favor =$\frac{1/2}{1-1/2}=\frac{1}{1}$ odds against =$\frac{1/2}{1-1/2}=\frac{1}{1}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.