Conditional Probability

The probability of event B occurring given that event A has already occurred, calculated as P(B|A) = P(A ∩ B) / P(A), wh

Probability

Conditional Probability Notation

The conditional probability P(A | B) is read 'the probability of A given B' and equals P(A ∩ B) / P(B), provided P(B) >

Probability

2.1: Addition Rule of Probability

The rule that P(A ∪ B) = P(A) + P(B) - P(A ∩ B), which gives the probability that at least one of the events A or B occu

Probability

2.1: Addition Rule of Probability

The rule that P(A ∩ B) = P(A) × P(B|A), giving the probability that both events A and B occur. For independent events, t

Probability

2.1: Addition Rule of Probability

Set theory provides the formal language for probability, where the sample space S is represented as a set, events as sub

Probability

2.1: Addition Rule of Probability

The sample space S (or Ω) is the universal set containing every possible outcome of an experiment. Any event is a subset

Probability

2.2: Independent Events

Events A and B are independent if P(A ∩ B) = P(A) × P(B), or equivalently, if P(B|A) = P(B) and P(A|B) = P(A).

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2.2: Independent Events

Events A and B are mutually exclusive if they cannot occur together, meaning P(A ∩ B) = 0 and P(A ∪ B) = P(A) + P(B).

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2.2: Independent Events

A two-way table (or contingency table precursor) presents frequencies or probabilities for two categorical variables, wi

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2.2: Independent Events

A tree diagram represents probability experiments as a series of branches, with each branch labeled with a probability.

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2.4: Venn Diagram

A graphical representation of sample spaces and events using overlapping circles or regions, where the area (or size) of

Probability

2.4: Venn Diagram

A visual representation of sequential events where branches show possible outcomes at each stage, with conditional proba

Probability

2.4: Venn Diagram

The addition law states P(A ∪ B) = P(A) + P(B) - P(A ∩ B); for mutually exclusive events, P(A ∪ B) = P(A) + P(B). The mu

Probability