Conditional Probability

Front

What is Conditional Probability?

Back

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

Front

How is Conditional Probability calculated?

Back

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

Front

What does P(A|B) represent?

Back

The probability of event A occurring given that event B has occurred.

Front

What is the formula for finding the probability of two independent events?

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P(A and B) = P(A) * P(B) for independent events.

Front

What is the difference between independent and dependent events?

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Independent events do not affect each other's probabilities, while dependent events do.

Front

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

Back

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

Front

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.

Front

What is Bayes' Theorem?

Back

A formula that describes the probability of an event based on prior knowledge of conditions related to the event.

Front

How do you interpret P(A|B) in a real-world context?

Back

It represents the likelihood of event A happening under the condition that event B is true.