determine the following probability question **Determine whether the events A and B are independent.**Given:- \( P(A^c) = 0.2 \)- \( P(B^c) = 0.4 \)- \( P(A \cap B) = 0.48 \)Options:- ( ) Yes- ( ) No**Explanation:**To determine if events \( A \) and \( B \) are independent, we need to check if the following condition holds:\[ P(A \cap B) = P(A) \cdot P(B) \]First, calculate \( P(A) \) and \( P(B) \):- \( P(A) = 1 - P(A^c) = 1 - 0.2 = 0.8 \)- \( P(B) = 1 - P(B^c) = 1 - 0.4 = 0.6 \)Now, calculate \( P(A) \cdot P(B) \):\[ P(A) \cdot P(B) = 0.8 \cdot 0.6 = 0.48 \]Since \( P(A \cap B) = 0.48 \), which equals \( P(A) \cdot P(B) \), the events \( A \) and \( B \) are independent.Correct answer:- ( X ) Yes

Answered: Determine whether the events A and B…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Determine whether the events A and B are independent. P(A) = 0.2, P(B) = 0.4, P(A n B) = 0.48 Yes Ο NO