Conditional Probability And Independence

Front

What is Conditional Probability?

Back

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

What is the formula for Conditional Probability?

Back

P(A | B) = P(A and B) / P(B), provided P(B) > 0.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What does it mean for two events to be Independent?

Back

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

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the formula for the probability of Independent Events?

Back

P(A and B) = P(A) * P(B).

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the Complement Rule in probability?

Back

The probability of an event not occurring is 1 minus the probability of the event occurring: P(A') = 1 - P(A).

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CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

How do you calculate the probability of multiple independent events?

Back

For independent events A, B, and C, the probability of all occurring is P(A and B and C) = P(A) * P(B) * P(C).

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the Total Probability Theorem?

Back

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: P(A | B) = [P(B | A) * P(A)] / P(B).

Front

What is the Law of Total Probability?

Back

It states that the total probability of an event can be found by considering all possible ways that event can occur.

Front

What is an example of Conditional Probability?

Back

If 60% of students like math and 30% of students like both math and science, then the probability of a student liking math given they like science is P(Math | Science) = P(Math and Science) / P(Science).

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5