# In class, it was stated that in order to show that more than two events are independent, you have to check every possible set of intersections. To illustrate this, consider rolling a fair 8-sided die and define the events:A1 = {1, 2, 3, 4} , A2 = {2, 6, 7, 8} and A3 = {1, 2, 3, 5}. Show that the triple intersection behaves as if these events were independent, but none of the pairs of events are independent.

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In class, it was stated that in order to show that more than two events are independent, you have to check every possible set of intersections. To illustrate this, consider rolling a fair 8-sided die and define the events:
A1 = {1, 2, 3, 4} , A2 = {2, 6, 7, 8} and A3 = {1, 2, 3, 5}. Show that the triple intersection behaves as if these events were independent, but none of the pairs of events are independent.

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Step 1

From the given information,

Step 2

Mutual Independence of three events for any three events A, B and C to be mutually independent the following two conditions must be met:

Step 3

The triple intersection behaves as if these events were independent, but...

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