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.

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.

Tags

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.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

How do you interpret P(B|A)?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the relationship between independent events and Conditional Probability?

Back

For independent events, P(A|B) = P(A). This means the occurrence of event B does not affect the probability of event A.

Tags

CCSS.HSS.CP.A.3

Front

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

Back

If A and B are independent, P(A ∩ B) = P(A) * P(B) = 0.5 * 0.4 = 0.2.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the Total Probability Theorem?

Back

The Total Probability Theorem states that if B1, B2, ..., Bn are mutually exclusive events that cover the entire sample space, then P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn).

Front

What is Bayes' Theorem?

Back

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

Front

How do you calculate the probability of a student playing a sport given they play an instrument?

Back

Use the formula for conditional probability: P(Sport|Instrument) = P(Sport ∩ Instrument) / P(Instrument).

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the significance of the intersection in Conditional Probability?

Back

The intersection P(A ∩ B) represents the probability that both events A and B occur simultaneously.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5