A coin is tossed twice. Consider the following events. A: Heads on the first toss. B: Heads on the second toss. C: The two tosses come out the same. (a) Show that A, B, C are pairwise independent but not independent. (b) Show that C is independent of A and B but not of An B.

A coin is tossed twice. Consider the following events. A: Heads on the first toss. B: Heads on the second toss. C: The two tosses come out the same. (a) Show that A, B, C are pairwise independent but not independent. (b) Show that C is independent of A and B but not of An B.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 39E: 39-40 Spinners A and B shown in the figure are spun at the same time. aAre the events spinner A...

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need help understanding independence in proability.

A coin is tossed twice. Consider the following events.
A: Heads on the first toss.
B: Heads on the second toss.
C: The two tosses come out the same.
(a) Show that A, B, C are pairwise independent but not independent.
(b) Show that C is independent of A and B but not of Añ B.

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Step 2: Determine pairwise independent and independent events

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Step 3: Determine sample space and events

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Step 4: Determine events are pairwise independent but not independent

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Step 5: Determine C is independent of A, B but not on A and B

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