Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 12 - Counting and Probability - Section 12.1 Counting - 12.1 Assess Your Understanding: 14

Answer

$n(A) = 50$

Work Step by Step

Given: $n(A∪B)= 60 , n(A∩B) = 40, n(A) = n(B)$ Use the formula $n(A \cup B) = n(A) + n(B) - n(A\cap B)$ to obtain: $n(A \cup B) = n(A) + n(B) - n(A\cap B) \\n(A \cup B) = n(A) + n(A) - n(A\cap B) \\n(A \cup B) = 2[n(A)] - n(A \cap B) \\60 = 2[n(A)] - 40 \\60+40=2[n(A)] \\100=2[n(A)] \\\frac{100}{2}=\frac{2[n(A)]}{2} \\50=n(A)$
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