In _________, different symbols are used to denote various elements and operations.
Probability Theory
Understanding these symbols is crucial for solving probability problems and interpreting mathematical notation.
Introduction to Probability
Probability. Represents the probability of an event occurring
P or Pr
Sample Space. The set of all possible outcomes of a random experiment
S
Events. Capital letters usually used to represent events, which are subsets of the sample space
A,B,C,…
Universal Set or Sample Space - The set of all possible outcomes, often used interchangeably with S
Ω
Probability of the Intersection of Events A and B. Probability that both events A and B occur at the same time
Pr(A∩B) or P(A∩B)P(AB)P(A∩B)
Union of Events. The union of A∪B A∪B represents the probability that either event A, event B, or both occur.
∪
Intersection of Events. The intersection A∩B represents the probability that both events A and B happen.
∩
Complement of Event A. Represents the probability that event A does not occur.
¬A or Ac
Conditional Probability. Probability of event A occurring, given that event B has occurred.
Pr(A∣B) or P(A∣B) P(A∣B)
Summation. Sum of probabilities or outcomes.
∑
Expected Value (Mean). Represents the average or expected value of a random variable.
μ
is a measure of how likely an event is to occur. It quantifies the uncertainty of events and is expressed as a number between 0 and 1, where:
Probability
indicates that the event is impossible
0
indicates that the event is certain.
1
is an action or process that produces a result. In probability, this result is uncertain.
Experiment
An ______ is a possible result of an experiment.
Outcomes
is the set of all possible outcomes of an experiment.
Sample Space
is a specific outcome or set of outcomes that we are interested in. It is a subset of the sample space.
Event
What are the Steps for solving probability problems?
- Identify the experiment
- List the sample space
- Identify the event
- Use the classical probability formula
