Applied Statistics and Probability for Engineers, 6th Edition

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

Chapter 2 - Section 2-6 - Independence - Exercises: 2-143

Answer

$B'$ and $A'$ are independent events

Work Step by Step

If $A'$ and $B'$ are independent, then $P(A'\cap B)= P(A')\times P(B)$. LHS= $P(A'\cap B)=P(B)-P(A\cap B)$. $P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}=0.3$ $P(A\cap B)=0.3\times 0.8=0.24$ $P(A'\cap B)=0.8-0.24=0.56$ RHS=$P(A')\times P(B)=(1-0.3)\times 0.8=0.56$
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