Conditional Probability

Front

What is Conditional Probability?

Back

The probability of an event occurring given that another event has already occurred.

Front

What is the formula for Conditional Probability?

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

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What does P(T | C) represent?

Back

The probability of event T occurring given that event C has occurred.

Front

If P(A) = 0.4 and P(B) = 0.5, what is P(A and B) if A and B are independent?

Back

P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.

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What is the meaning of P(Female | Part-time)?

Back

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

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How do you calculate P(A | B) using a frequency table?

Back

Count the number of occurrences of A and B together, then divide by the total occurrences of B.

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What is the complement of an event?

Back

The complement of an event A is the event that A does not occur, denoted as A'.

Front

If P(A) = 0.3, what is P(A')?

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P(A') = 1 - P(A) = 1 - 0.3 = 0.7.

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What is the significance of a conditional probability being greater than or less than 0.5?

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If P(A|B) > 0.5, event A is more likely to occur given B; if < 0.5, A is less likely.

Front

What is Bayes' Theorem?

Back

A way to find a conditional probability when you know the reverse conditional probability and the marginal probabilities.