Applied Statistics and Probability for Engineers, 6th Edition

Published by Wiley
ISBN 10: 1118539710
ISBN 13: 978-1-11853-971-2

Chapter 2 - Section 2-5 - Multiplication and Total Probability Rules - Exercises - Page 49: 2-137

Answer

$0.2$ (if red is one of the 4 colors) $0$ otherwise

Work Step by Step

If red is not one of the 4 colors then probability of having a red ad is 0. Now suppose red is one of the 4 colors, then Let A be the event that the random color chosen is red and B be the event that the selected font is the smallest one We have to find $P(A\cap B')$ Since the colors are randomly selected the probability of getting each is $\frac{1}{4}$ Hence $P(A)=\frac{1}{4}$ Similarly the probability of each font getting chosen is $P(B)=\frac{1}{5}$ Now $P(A\cap B')=P(A)P(B')=P(A)[1-P(B)]=\frac{1}{4}[1-\frac{1}{5}]=\frac{1}{4}\cdot\frac{4}{5}=\frac{1}{5}$
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