All Flashcards
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 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 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.