Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 11 - Counting Methods and Probability Theory - 11.6 Events Involving Not and Or; Odds - Exercise Set 11.6: 37

Answer

$\frac{4}{5}$

Work Step by Step

If A and B are not mutually exclusive events, then P(A or B) = P(A)+P(B) - P(A and B) We are asked to find the probability that a randomly selected person on the faculty is a teaching assistant or a female. P(choosing a teaching assistant) = $\frac{No. Of teaching assistant}{Total Faculty }$ =$\frac{21}{40}$ P(choosing a female)= $\frac{No. of females}{Total Faculty}$ = $\frac{18}{40}$ P(a TA and a female) = $\frac{7}{40}$ P(a TA or a female) = P(a TA) +P(a female) - P(a TA and a female) =$\frac{21}{40}$ + $\frac{18}{40}$ - $\frac{7}{40}$ =$\frac{21+18 -7}{40}$ = $\frac{32}{40}$ = $\frac{4}{5}$
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