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3.9. Consider two independent tosses of a fair coin. Let A be the event that the first toss results in heads, let B be the event that the second toss results in heads, and let C be the event that in both tosses the coin lands on the same side. Show that the events A, B, and C are pairwise independent that is, A and B are independent, A and C are independent, and B and Care independent-but not independent.

3.9. Consider two independent tosses of a fair coin. Let A be the event that the first toss results in heads, let B be the event that the second toss results in heads, and let C be the event that in both tosses the coin lands on the same side. Show that the events A, B, and C are pairwise independent that is, A and B are independent, A and C are independent, and B and Care independent-but not independent.

A First Course in Probability (10th Edition)
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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3.9. How can I show that ?

**Exercise 3.9: Coin Toss Independence** Consider two independent tosses of a fair coin. Let \( A \) be the event that the first toss results in heads, let \( B \) be the event that the second toss results in heads, and let \( C \) be the event that in both tosses the coin lands on the same side. Show that the events \( A \), \( B \), and \( C \) are pairwise independent—that is, \( A \) and \( B \) are independent, \( A \) and \( C \) are independent, and \( B \) and \( C \) are independent—but not independent in groups of more than two.
Transcribed Image Text:**Exercise 3.9: Coin Toss Independence** Consider two independent tosses of a fair coin. Let \( A \) be the event that the first toss results in heads, let \( B \) be the event that the second toss results in heads, and let \( C \) be the event that in both tosses the coin lands on the same side. Show that the events \( A \), \( B \), and \( C \) are pairwise independent—that is, \( A \) and \( B \) are independent, \( A \) and \( C \) are independent, and \( B \) and \( C \) are independent—but not independent in groups of more than two.
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