College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 10 - Section 10.1 - Counting - 10.1 Assess Your Understanding: 32

Answer

25.6 million females 18 years old and older are widowed or divorced. 91.8 million females 18 years old and older are married, widowed, or divorced.

Work Step by Step

Set $A$ is the females 18 years old and older who are married, set $B$ is the females 18 years old and older who are widowed, and set $C$ is the females 18 years old and older who are divorced. The first question asks for the union of sets $B$ and $C$ Using the Counting Formula for sets: $n(B\cup C)=n(B)+n(C)-n(B\cap C)$ According to the survey, there isn't anybody who is both widowed and divorced; therefore, $n(B\cap C)=0$ $n(B\cup C)=11.2+14.4-0=25.6$ 25.6 million females 18 years old and older are widowed or divorced. The second question asks for the union of sets $A$, $B$, and $C$. Using the Counting Formula for sets: $n(A\cup B\cup C)=n(A)+n(B+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)$ According to the survey there isn't anybody who is in either intersection of these sets; therefore: $n(A\cup B\cup C)=n(A)+n(B+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)=66.2+11.2+14.4-0-0-0+0=91.8$ 91.8 million females 18 years old and older are married, widowed, or divorced.
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