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.
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).