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 calculated?

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 does P(A | B) represent?

Back

The probability of event A occurring given that event B has occurred.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

If P(A) = 1/2 and P(B) = 1/3, what is P(A and B) if A and B are independent?

Back

P(A and B) = P(A) * P(B) = (1/2) * (1/3) = 1/6.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the formula for the total probability theorem?

Back

P(A) = Σ P(A | B_i) * P(B_i) for all i, where B_i are mutually exclusive events.

Front

What is the complement rule in probability?

Back

P(A') = 1 - P(A), where A' is the complement of event A.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the probability of rolling an even number on a fair die?

Back

P(even) = 3/6 = 1/2.

Tags

CCSS.7.SP.C.7B

Front

What is the probability of rolling a number less than 5 given that the number is even?

Back

P(less than 5 | even) = 2/3.

Tags

CCSS.HSS.CP.B.6

Front

What is the probability of rolling a 2 given that the number rolled is greater than 3?

Back

P(2 | greater than 3) = 0.

Tags

CCSS.HSS.CP.B.6

Front

What is the probability of a student playing a sport given they play an instrument?

Back

P(sport | instrument) = 3/14.

Tags

CCSS.HSS.CP.B.6