Sample Space, Events and Addition Rule
Probability assigns numbers in [0, 1] to events of a sample space, with P(A or B) = P(A) + P(B) - P(A and B).
What is Sample Space, Events and Addition Rule?
Probability assigns numbers in [0, 1] to events of a sample space, with P(A or B) = P(A) + P(B) - P(A and B).
Key formula / rule: Probabilities of all outcomes in a sample space sum to 1.
Key points
- Define a sample space for a described random experiment.
- Compute probabilities of compound events using the addition rule.
Common exam trap
Adding probabilities of events that are not mutually exclusive.
Definitions
- Term
Sample Space, Events and Addition Rule
- Meaning
Probability assigns numbers in [0, 1] to events of a sample space, with P(A or B) = P(A) + P(B) - P(A and B).
- Term
Sample Space, Events and Addition Rule — explanation
- Meaning
Careful description of the sample space settles most elementary probability questions before any formula appears. The addition rule corrects for double counting the overlap.
Learning objectives
Define a sample space for a described random experiment.
Compute probabilities of compound events using the addition rule.
Formulae
- Key point
Probabilities of all outcomes in a sample space sum to 1.
- Key point
Mutually exclusive events have zero intersection probability.
- Key point
The complement rule gives P(not A) = 1 - P(A).
Prerequisites
MAT-U1-PC-T1-S1-C2
Common mistakes
Adding probabilities of events that are not mutually exclusive.
Assuming equally likely outcomes when the experiment does not justify it.
Keywords
Sample
Space
Events
Addition
Practice preview
Given P(A) = 0.4, P(B) = 0.6, and P(A ∩ B) = 0.2, find P(A U B).…
easy
What is the sample space when two fair coins are tossed simultaneously?…
easy
If A and B are two mutually exclusive events such that P(A) = 0.3 and P(B) = 0.5, what is P(A U B)?…
easy