For AI agents: use /llms.txt for the Nakafa content index.
Imagine you have two choices, but you can only pick one, not both at the same time. Well, in the world of probability, this is similar to the concept of Mutually Exclusive Events (other cool names: Disjoint Events).
Two events (let's call them event and event ) are said to be mutually exclusive if both events cannot possibly occur at the same time in a single trial. Simply put, if happens, cannot happen. If happens, cannot happen.
The main characteristic is just that: cannot happen simultaneously. There's no outcome that can belong to event and event at the same time.
Because events and cannot happen together if they are mutually exclusive, the probability of both occurring simultaneously is zero!
We can write the probability of event " and " (both occurring) as:
Or using the intersection symbol:
Remember, if they are mutually exclusive, their intersection is empty, so the probability is zero!
So, how do we calculate the probability of event happening OR event happening if and are mutually exclusive?
Since they can't happen together, we simply add the probabilities of each individual event.
The formula becomes very easy:
Or using the union symbol:
This is the Special Addition Rule which applies ONLY to mutually exclusive events. (If the events are not mutually exclusive, there's a slightly different formula).
To understand better, look at these examples:
Coin Toss:
The event of getting "Heads" and the event of getting "Tails". They can't happen together, right?
Rolling a Die (once):
Look at two pairs of events:
Drawing a Card (once):
Use the same idea for card events:
