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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross
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Consider two independent tosses of a fair coin. Let Abe

Chapter 3, Problem 9TE

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QUESTION:

Problem 9TE

Consider two independent tosses of a fair coin. Let Abe 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, Aand Barc independent, Aand C are independent, and Band Care independent—but not independent.

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QUESTION:

Problem 9TE

Consider two independent tosses of a fair coin. Let Abe 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, Aand Barc independent, Aand C are independent, and Band Care independent—but not independent.

ANSWER:

Step 1 of 2

A coin tosses two times.

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.

We have to show that the events A, B, and C are pairwise independent but not independent.

 

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