Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 7 - Section 7.5 - Conditional Probability and Independence - Exercises - Page 507: 31

Answer

Independent

Work Step by Step

We know that both $A$ and $B$ are independent events when it satisfies the following condition such that $P(A \cap B)=P(A) P(B) ~~~(1)$ Here, $A$ denotes the red die is $1, 2$ or 3 and $B$ denotes the green die is even. We can see that $P(A)=\dfrac{n(A)}{n(B)}=\dfrac{18}{36}=\dfrac{1}{2}$ and $P(B)=\dfrac{n(B)}{n(S)}=\dfrac{18}{36}=\dfrac{1}{2}$ Next, we find that there are nine outcomes that can be possible. So, $P(A \cap B)=\dfrac{n(A \cap B)}{n(S)}=\dfrac{9}{36}=\dfrac{1}{4}$ Also, $P(A \cap B)=\dfrac{1}{4}$ and $P(A) P(B)=(\dfrac{1}{2})(\dfrac{1}{2})=\dfrac{1}{4}$ This means that condition (1) is satisfied. So, both $A$ and $B$ are independent events.
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