Probability Theory
What is Probability Theory?
The set of all possible outcomes of a random experiment.
Key formula / rule: Probability of an Event
Key points
- Define and understand basic probability terms.
- Calculate probabilities of simple and compound events.
- Apply rules of probability (addition, multiplication).
- Understand and calculate conditional probability.
Common exam trap
Confusing mutually exclusive and independent events.
Definitions
- Term
Sample Space (S)
- Meaning
The set of all possible outcomes of a random experiment.
- Term
Event (E)
- Meaning
A subset of the sample space, representing a specific outcome or set of outcomes.
- Term
Probability
- Meaning
A numerical measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
- Term
Mutually Exclusive Events
- Meaning
Events that cannot occur at the same time; their intersection is empty.
- Term
Independent Events
- Meaning
Events where the occurrence of one does not affect the probability of the other occurring.
- Term
Conditional Probability
- Meaning
The probability of an event occurring, given that another event has already occurred.
Learning objectives
Define and understand basic probability terms.
Calculate probabilities of simple and compound events.
Apply rules of probability (addition, multiplication).
Understand and calculate conditional probability.
Recognize independent and dependent events.
Formulae
- Name
Probability of an Event
- Note
Applies to equally likely outcomes.
- Expression
P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)
- Name
Addition Rule
- Note
Probability of A or B occurring.
- Expression
P(A U B) = P(A) + P(B) - P(A ∩ B)
- Name
Addition Rule (Mutually Exclusive)
- Note
If events A and B cannot occur together (P(A ∩ B) = 0).
- Expression
P(A U B) = P(A) + P(B)
- Name
Multiplication Rule
- Note
Probability of both A and B occurring.
- Expression
P(A ∩ B) = P(A) * P(B|A)
- Name
Multiplication Rule (Independent Events)
- Note
If events A and B are independent.
- Expression
P(A ∩ B) = P(A) * P(B)
- Name
Conditional Probability
- Note
Probability of A given that B has occurred.
- Expression
P(A|B) = P(A ∩ B) / P(B)
Prerequisites
Basic Arithmetic
Set Theory Concepts (Union, Intersection, Complement)
Basic Algebra
Common mistakes
Confusing mutually exclusive and independent events.
Incorrectly applying the addition or multiplication rule.
Misinterpreting conditional probability.
Assuming events are independent when they are not.
Calculation errors in determining sample space size.
Keywords
Probability
Random Experiment
Sample Space
Event
Outcomes
Mutually Exclusive
Independent
Conditional Probability
Addition Rule
Multiplication Rule
Practice preview
From a well-shuffled deck of 52 playing cards, one card is drawn at random. What is the probability that the card drawn is a King?…
medium
Which of the following values CANNOT be a probability of an event?…
easy
A single fair die is rolled. What is the probability of getting an even number?…
easy