Conditional Probability

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What is Conditional Probability?

Back

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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How is Conditional Probability calculated?

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

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What does P(Female | Part-time) represent?

Back

The probability that a student is female given that they are a part-time student.

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If P(A|B) = 0.67, what does this imply?

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It implies that there is a 67% chance of event A occurring given that event B has occurred.

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What is the formula for Bayes' Theorem?

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P(A|B) = [P(B|A) * P(A)] / P(B), used to find conditional probabilities.

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What is the significance of the Venn Diagram in probability?

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

Front

What does P(Full-time | Male) indicate?

Back

The probability that a student is full-time given that they are male.

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How do you interpret P(Sandals|Pants) = 2/7?

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There is a 2 out of 7 chance that a student is wearing sandals given that they are wearing pants.

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What is the relationship between independent events and conditional probability?

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If two events A and B are independent, then P(A|B) = P(A). The occurrence of B does not affect the probability of A.

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What does it mean if P(A|B) = 1?

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It means that event A will definitely occur if event B has occurred.