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 reads as 'the probability of A given B'.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the formula for Conditional Probability?

Back

The formula for Conditional Probability is P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B occurring.

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CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What does P(A|B) represent?

Back

P(A|B) represents the probability of event A occurring given that event B has occurred.

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CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

How do you interpret P(A|B) = 0.5?

Back

This means that if event B occurs, there is a 50% chance that event A will also occur.

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CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the relationship between P(A|B) and P(B|A)?

Back

P(A|B) and P(B|A) are not equal; they depend on the individual probabilities of A and B. They can be related through Bayes' Theorem.

Front

What is Bayes' Theorem?

Back

Bayes' Theorem relates the conditional and marginal probabilities of random events. It is expressed as P(A|B) = [P(B|A) * P(A)] / P(B).

Front

What is the significance of the Venn Diagram in Conditional Probability?

Back

A Venn Diagram visually represents the relationships between different events, helping to illustrate the intersections and unions of events, which are crucial for calculating probabilities.

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CCSS.HSS.CP.A.1

Front

How do you calculate P(A ∩ B)?

Back

P(A ∩ B) can be calculated using the formula P(A ∩ B) = P(A|B) * P(B) or P(A ∩ B) = P(B|A) * P(A).

Front

What is the meaning of independent events in probability?

Back

Two events A and B are independent if the occurrence of one does not affect the probability of the other, meaning P(A|B) = P(A) and P(B|A) = P(B).

Tags

CCSS.HSS.CP.A.3

Front

What is the probability of event A if P(A) = 0.3 and P(B) = 0.4, and A and B are independent?

Back

If A and B are independent, P(A ∩ B) = P(A) * P(B) = 0.3 * 0.4 = 0.12.

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CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4