Conditional Probability

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What is Conditional Probability?

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The probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads 'the probability of A given B'.

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What is the formula for Conditional Probability?

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P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both A and B occurring.

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What does P(A|B) represent?

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It represents the probability of event A occurring given that event B has occurred.

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If P(A) = 0.5 and P(B) = 0.4, what is P(A|B) if P(A ∩ B) = 0.2?

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P(A|B) = P(A ∩ B) / P(B) = 0.2 / 0.4 = 0.5.

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What is the relationship between independent events and Conditional Probability?

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For independent events, P(A|B) = P(A). The occurrence of B does not affect the probability of A.

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How do you interpret P(B|A)?

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It is the probability of event B occurring given that event A has occurred.

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What is the Law of Total Probability?

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It states that if B1, B2, ..., Bn are mutually exclusive events that cover the entire sample space, then P(A) = Σ P(A|Bi)P(Bi).

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What is Bayes' Theorem?

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Bayes' Theorem relates the conditional and marginal probabilities of random events. It is given by P(A|B) = [P(B|A) * P(A)] / P(B).

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What is an example of Conditional Probability in real life?

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Determining the probability of a person having a disease given a positive test result.

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What is the significance of Venn Diagrams in Conditional Probability?

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Venn Diagrams visually represent the relationships between different events, helping to understand intersections and unions.