All Flashcards
What is Conditional Probability?
The probability of an event occurring given that another event has already occurred.
Define Intersection (A ∩ B).
The event where both A and B occur.
Define Union (A ∪ B).
The event where either A or B or both occur.
What is a Tree Diagram?
A diagram that shows outcomes in a series of events, where each branch represents a different outcome.
What is a Venn Diagram?
A diagram showing relationships between sets of outcomes, where the area of each circle represents the probability of that set.
What is the formula for Conditional Probability P(B | A)?
P(B | A) = P(A ∩ B) / P(A)
What is the General Multiplication Rule?
P(A and B) = P(A) * P(B | A)
How do you calculate P(A ∩ B) if P(A), P(B|A) are known?
P(A ∩ B) = P(A) * P(B|A)
How do you calculate P(A) if P(B|A) and P(A ∩ B) are known?
P(A) = P(A ∩ B) / P(B|A)
What is P(B|A) if events A and B are independent?
P(B|A) = P(B)
What are the differences between Tree Diagrams and Venn Diagrams?
Tree Diagrams: Show sequential events, good for conditional probabilities. | Venn Diagrams: Show relationships between sets, good for intersections and unions.
What are the differences between P(A and B) and P(A | B)?
P(A and B): Probability of both A and B occurring. | P(A | B): Probability of A occurring given that B has already occurred.
What are the differences between independent and dependent events?
Independent Events: Occurrence of one does not affect the other. | Dependent Events: Occurrence of one affects the probability of the other.
What are the differences between joint and conditional probability?
Joint Probability: Probability of two events occurring together. | Conditional Probability: Probability of one event occurring given that another has already occurred.
What is the difference between Probability Histograms and Plots?
Probability Histograms: Bar graphs showing the probability of different outcomes. | Plots: Graphs showing the relationship between the probability of an event and a continuous variable.