Conditional Probability

Front

What is Conditional Probability?

Back

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

Front

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 probability of both events occurring and P(B) is the probability of event B.

Front

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

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P(Female | Part-time) represents the probability that a student is female given that they are a part-time student.

Front

If P(A|B) = 15/31, what does this imply?

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This implies that if we know a student is part-time, there is a 15 out of 31 chance that the student is female.

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What is the formula for finding P(Male | Full-time)?

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P(Male | Full-time) = P(Male and Full-time) / P(Full-time).

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What does P(Pizza | Senior) indicate?

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P(Pizza | Senior) indicates the probability that a senior student prefers pizza.

Front

If P(Sandals | Pants) = 2/7, what does this mean?

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This means that among students wearing pants, 2 out of 7 are wearing sandals.

Front

What is the significance of the denominator in conditional probability?

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The denominator represents the total number of occurrences of the condition (event B) under which we are calculating the probability.

Front

How do you interpret P(Full-time | Male) = 3/7?

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This means that if we know a student is male, there is a 3 out of 7 chance that the student is full-time.

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What is the relationship between joint probability and conditional probability?

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Joint probability P(A and B) can be expressed in terms of conditional probability: P(A and B) = P(A|B) * P(B).