What is the definition of probability?
The basis for inferential statistics
Probability is used to determine the likelihood of events occurring.
What are the two methods of assigning probabilities?
- Classical method
- Relative frequency of occurrence method
Each method has different approaches to determining probabilities.
In the classical method, how is probability determined?
By dividing the number of favorable outcomes by the total number of possible outcomes
This method is based on laws and rules and can be determined before the experiment.
What does the relative frequency of occurrence method rely on?
Cumulative historical data
This method is not based on laws and rules but rather on past occurrences.
Define experiment in the context of probability.
A process that produces outcomes (events)
An experiment can involve various scenarios, such as rolling dice or conducting surveys.
What is an event?
An outcome of the experiment
Events can be elementary or composite, depending on their complexity.
What are elementary events?
Events that cannot be broken down into other events
For example, rolling a 1 on a die is an elementary event.
What are mutually exclusive events?
Events that cannot occur simultaneously
An example is getting heads or tails in a coin toss.
What are independent events?
One event does not affect another event
For instance, the outcome of one coin toss does not influence the next.
What are complementary events?
All events that did not happen
If an event occurs, its complement includes all other possible outcomes.
What is a sample space?
A complete listing of all elementary events for an experiment
It represents all possible outcomes.
What does the Mn counting rule state?
If one task can be done in m ways and another in n ways, then both can be done in m × n ways
This rule helps in calculating the total number of outcomes for multiple tasks.
What is set notation?
Uses braces { } to group elements
Set notation is essential for defining sets in probability.
What does a Venn diagram illustrate?
Relationships between sets
Overlapping circles show common elements between sets.
What does Union (X ∪ Y) represent?
Combines all elements from both sets (X OR Y)
It includes all unique elements from both sets.
What does Intersection (X ∩ Y) represent?
Shows elements common to both sets (X AND Y)
It includes only the elements that are present in both sets.
What is the general law of addition used for?
To find the probability of X or Y (or both) happening
It involves subtracting the overlap to avoid double counting.
What is conditional probability?
The chance of something happening only within a certain group
It focuses on a subset of cases where a condition is already true.
What does the general law of multiplication calculate?
The probability of two things happening together (joint probability)
It is used when determining the likelihood of multiple events occurring simultaneously.
What is the law of probability?
How to find the probability of X happening given Y already happened
It assesses the relationship between two events.
What is Bayes’ rule?
How we update our guesses when we get new information
It allows for revising probabilities based on new evidence.
What is a discrete random variable?
A variable that can take on a finite or countably infinite number of possible values
Examples include counts of people or items.
What is a continuous random variable?
A variable that can take on values at every point over a given interval
Examples include measurements like height or weight.
What is a binomial distribution?
Used to count how many successes occur in a fixed number of trials (n)
Each trial has only two outcomes: success or failure.
