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 'the probability of A given B'.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

How is Conditional Probability calculated?

Back

Conditional Probability is calculated using the formula: P(A|B) = P(A and B) / P(B), where P(A and B) is the joint probability of both events occurring.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What does P(Male | Full-time) represent?

Back

P(Male | Full-time) represents the probability that a student is male given that they are a full-time student.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

If P(Studies) = 8/9 and P(Passes and Studies) = 3/5, how do you find P(Passes | Studies)?

Back

Use the formula: P(Passes | Studies) = P(Passes and Studies) / P(Studies) = (3/5) / (8/9) = 27/40.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the significance of the denominator in Conditional Probability?

Back

The denominator in Conditional Probability represents the total probability of the condition being true, which normalizes the probability of the event of interest.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the formula for finding P(A | B) when given a contingency table?

Back

P(A | B) = (Number of outcomes where A and B occur) / (Total number of outcomes where B occurs).

Tags

CCSS.HSS.CP.A.4

Front

What does P(Plays Sport | Does Not Play Instrument) indicate?

Back

P(Plays Sport | Does Not Play Instrument) indicates the probability that a student plays a sport given that they do not play an instrument.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

How do you interpret P(Female | Part-time)?

Back

P(Female | Part-time) indicates the probability that a student is female given that they are a part-time student.

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), meaning the occurrence of B does not affect the probability of A.

Tags

CCSS.HSS.CP.A.3

Front

What is the role of joint probability in Conditional Probability?

Back

Joint probability, P(A and B), is essential in calculating Conditional Probability as it quantifies the likelihood of both events occurring together.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5