Mutual Independence for 3 events

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SUMMARY

The discussion focuses on proving the mutual independence of events A and (B intersection C). It clarifies that A and (B intersection C) represent two distinct events, while A union (B intersection C) describes a single event. The concept of independence applies only when comparing two or more events, making the first statement relevant for analysis. Understanding these distinctions is crucial for correctly interpreting the question posed.

PREREQUISITES
  • Basic probability theory
  • Understanding of event notation in probability
  • Knowledge of mutual independence concepts
  • Familiarity with set operations (union and intersection)
NEXT STEPS
  • Study the formal definition of mutual independence in probability theory
  • Learn how to apply the multiplication rule for independent events
  • Explore examples of event independence using probability trees
  • Investigate the implications of independence in statistical modeling
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Students of probability theory, statisticians, and anyone interested in understanding the principles of event independence in probability contexts.

madness26
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how do i prove that A and (B intersection C) are mutually independent?
first of all how do i even read that question, is it read: A union (B intersection C) ??
 
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madness26 said:
how do i prove that A and (B intersection C) are mutually independent?
first of all how do i even read that question, is it read: A union (B intersection C) ??

To start with you need to know something about A, B, and C.

A and (B intersection C)
describes two events.
A union (B intersection C)
describes one event.

The notion of independence is meaningful only when discussing two or more events. Therefore only the first statement is meaningful.
 

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