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 A and B?

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P(A and B) = P(A) * P(B) if A and B are independent.

Front

If P(A) = 0.3 and P(B) = 0.4, what is P(A and B) if A and B are independent?

Back

P(A and B) = 0.3 * 0.4 = 0.12.

Front

What is the complement of an event?

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

Front

If P(A) = 0.5, what is P(A')?

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P(A') = 1 - P(A) = 1 - 0.5 = 0.5.

Front

What is Bayes' Theorem?

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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.

Front

What is the significance of the denominator in the conditional probability formula?

Back

The denominator, P(B), represents the total probability of the condition under which we are calculating the probability of A.