EXTRA CREDIT: Extending the Addition Rule (Due April 6)

Extending the Addition Rule (+5 points)

In the last lesson and assignment, we learned how to use the addition rule for two events. For two events that are not disjoint, we visualized the addition rule as follows:

$$P(A \bigcup B) = P(A) + P(B) - P(A \bigcap B)$$

We only looked at probability questions that examined two events. But how does the addition rule change when there are three events? 

Using what you know about how the addition rule was created for two events, correctly write the rule for three non-disjoint events and explain it. In other words:

$$P(A \bigcup B \bigcup C) = ?$$