Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 4 - Probability - 4-4 Multiplication Rule: Basics - Basic Skills and Concepts: 6

Answer

$\frac{1}{4}.$, independent

Work Step by Step

Two events are dependent, if the outcome of one effects the outcome of the other. Here the events are independent, because the gender of the first child doesn't affect the second one, hence here sampling was done without replacement and $P(B|A)=P(B)$. $P(A \cap B)=P(A)\cdot P(B|A)$. Hence $P(A \cap B)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}.$
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