Conditional Probability

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What is Conditional Probability?

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

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What is the formula for Conditional Probability?

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The formula for Conditional Probability is P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B occurring.

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What does P(A|B) represent?

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P(A|B) represents the probability of event A occurring given that event B has occurred.

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How do you interpret P(A|B) = 0.5?

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This means that if event B occurs, there is a 50% chance that event A will also occur.

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What is the relationship between P(A|B) and P(B|A)?

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P(A|B) and P(B|A) are not equal; they depend on the individual probabilities of A and B. They can be related through Bayes' Theorem.

Front

What is Bayes' Theorem?

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

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What is the significance of the Venn Diagram in Conditional Probability?

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A Venn Diagram visually represents the relationships between different events, helping to illustrate the intersections and unions of events, which are crucial for calculating probabilities.

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How do you calculate P(A ∩ B)?

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P(A ∩ B) can be calculated using the formula P(A ∩ B) = P(A|B) * P(B) or P(A ∩ B) = P(B|A) * P(A).

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What is the meaning of independent events in probability?

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Two events A and B are independent if the occurrence of one does not affect the probability of the other, meaning P(A|B) = P(A) and P(B|A) = P(B).

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What is the probability of event A if P(A) = 0.3 and P(B) = 0.4, and A and B are independent?

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If A and B are independent, P(A ∩ B) = P(A) * P(B) = 0.3 * 0.4 = 0.12.