For AI agents: use /llms.txt for the Nakafa content index.
We learned about mutually exclusive events that can't happen together (like turning left and right at the same time). Now, let's talk about Non-Mutually Exclusive Events. These are two (or more) events that CAN happen at the same time in a single experiment.
This means it's possible to get an outcome that belongs to event and also belongs to event .
Simple Examples:
You draw one card from a standard deck.
Rolling a Die (once):
In non-mutually exclusive events, there's a part that belongs to both events simultaneously. This part is called the intersection.
Because there is an intersection, the probability of event AND B happening together is greater than zero.
Or using the intersection symbol:
This is very different from mutually exclusive events, where .
Since there's a chance that events and can happen together, we can't just add to find .
Why not? Because if we simply add them, the intersection part () gets counted twice, once in and again in .
To get the correct calculation, we must subtract the probability of the intersection that was double-counted. This gives us the General Addition Rule for probability:
Or using the union and intersection symbols:
This formula works generally, for both mutually exclusive and non-mutually exclusive events. (If they are mutually exclusive, is zero, so the formula simplifies back to ).
Let's use the card example:
So, the probability of getting a Heart OR a King is:
See? We subtract so the King of Hearts isn't counted twice.
