The Lesson
Two or more events are mutually exclusive if they cannot happen at the same time.A Real Example of Mutually Exclusive Events
It is easier to understand mutually exclusive events with an example.Tossing a Coin
A tossed coin can either land as Heads or as Tails. It cannot land as both at the same time. Heads and Tails are mutually exclusive events.
Exhaustive Events
A set of events are exhaustive if they include all possible outcomes. Heads and Tails are exhaustive events because they are all the possible outcomes of tossing a coin.Probabilities of Exhaustive Events Sum to 1
If a set of mutually exlusive events are exhaustive, their probabilities add up to 1. If a coin is tossed, it must land as either Heads or Tails. That is a certainty.
P(Heads) + P(Tails) = 1
A Note on Notation
The probability of an event can be written as:
P(Event)
A letter or symbol can be used to represent an event.
For example, let H be the event that a coin lands on Heads when it has been tossed.
We can denote the probability of getting heads as:
P(H)