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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.
Explain the concept of conditional probability.
The probability of an event occurring given that another event has already happened. It narrows the focus to the world where the given event has occurred.
Explain how tree diagrams are used to visualize probability.
Tree diagrams show outcomes in a series of events. Each branch represents a different outcome, and branch size can represent probability, especially conditional probabilities.
Explain how Venn diagrams are used to visualize probability.
Venn diagrams show relationships between sets of outcomes. The area of each circle represents the probability of that set, visualizing intersections (AND) and unions (OR).
Explain how two-way tables are used to visualize probability.
Two-way tables organize data into rows and columns, showing the frequency of different outcomes. They're excellent for calculating joint and conditional probabilities.
Explain the meaning of 'AND' and 'OR' in probability.
'AND' means intersection (both events occur), while 'OR' means union (either or both events occur).