Types of Probability Events
Mutually exclusive events cannot occur together in the outcome being considered. Dependent events have probabilities that change when information about another event is taken into account. These are different relationships, not an exhaustive division of events.
THE IDEA
Types of Probability Events
Two useful relationships to distinguish when analyzing probabilities are mutual exclusivity and dependence.
Mutually exclusive events cannot both occur in the outcome being considered. On a single ordinary coin toss, heads excludes tails. On a roll of a standard die, only one face can “come up.” The same idea applies when a decision permits only one of several alternatives.
Dependent events are events for which learning that one occurred changes the probability of the other. A sequence can involve dependence, but dependence does not require events to happen in sequence.
The source illustrates a sequence with a conventional key-start car: inserting the key permits turning it; turning it activates the starter; the starter rotates the engine so it can ignite. Modeling such a process requires considering the chance of each step succeeding given what has happened so far.
Mutually exclusive events can also be dependent: learning that one occurred rules out the other. Specify the relationship relevant to the calculation instead of treating the labels as competing categories.
When to use it
Calculating probabilities for mutually exclusive outcomes of a specified coin toss, die roll, or card draw.
Modeling a process whose next step depends on the success of earlier steps.
Decision analysis when choosing between options that are mutually exclusive.
Risk assessment for events that have conditional dependencies.
FROM THEORY TO EVERYDAY LIFE
In practice
Coin Toss
A coin toss involves mutually exclusive outcomes: heads or tails. One outcome precludes the other.
Starting a Car
Starting an engine involves conditionally dependent events: inserting the key conditions turning the key, which conditions the starter, which conditions ignition.
A MOMENT TO REFLECT
Put it to work.
Can you think of a real-life decision that involves mutually exclusive events? How does understanding that help you evaluate probabilities?
In what situations does the occurrence of one event depend on another? How can you model this with conditional probability?
How might confusing mutually exclusive events with conditionally dependent events lead to errors in reasoning?
CONTINUE THE CONVERSATION
Source texts
- The Thinkers Toolkit by Morgan D Jones