Conditional Probability

Front

What is Conditional Probability?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

How is Conditional Probability mathematically represented?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the formula for Total Probability?

Back

P(A) = P(A|B)P(B) + P(A|¬B)P(¬B), where ¬B is the complement of B.

Front

What does P(A and B) represent?

Back

The probability that both events A and B occur.

Front

What is the difference between independent and dependent events?

Back

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

Tags

CCSS.HSS.CP.A.5

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) = 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 probability of drawing a red marble from a bag with 3 red, 2 blue, and 4 yellow marbles?

Back

P(Red) = 3/9 = 1/3.

Tags

CCSS.7.SP.C.7B

Front

What is the probability that a student plays on a sports team given they play an instrument?

Back

P(Sports Team | Instrument) = 0.7273.

Tags

CCSS.HSS.CP.B.6

Front

What is Bayes' Theorem?

Back

A way to find a conditional probability when you know the reverse conditional probability: P(A|B) = [P(B|A) * P(A)] / P(B).

Front

What is the probability that a person speaks French given they are a girl?

Back

P(French | Girl) = 0.4.

Tags

CCSS.HSS.CP.B.6