Mutual Independence for 3 events

In summary, to prove that A and (B intersection C) are mutually independent, you need to understand the events A, B, and C. A and (B intersection C) describe two events, while A union (B intersection C) describes one event. The concept of independence is only applicable when discussing two or more events, making the first statement the only one that is relevant for proving mutual independence.
  • #1
madness26
1
0
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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  • #2
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.
 

Related to Mutual Independence for 3 events

1. What is mutual independence for 3 events?

Mutual independence for 3 events refers to the concept that the occurrence of one event does not affect the probability of the other two events occurring. In other words, the events are all independent of each other.

2. How is mutual independence for 3 events calculated?

Mutual independence for 3 events can be calculated by using the formula P(A ∩ B ∩ C) = P(A) * P(B) * P(C), where A, B, and C are three independent events.

3. Can events be mutually independent if they are not independent pairwise?

Yes, it is possible for three events to be mutually independent even if they are not independent pairwise. This means that while any two events may be dependent, when all three events are considered together, they are independent.

4. What is the difference between mutual independence and pairwise independence?

The main difference between mutual independence and pairwise independence is that mutual independence refers to the independence of all three events together, while pairwise independence only refers to the independence of any two events.

5. How is mutual independence for 3 events related to conditional independence?

Mutual independence for 3 events is a special case of conditional independence, where the events are conditionally independent given any subset of events. In other words, the events are still independent even when considering the occurrence of other events.

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