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### Math

## Common Core Math

# High School: Statistics & Probability: Conditional Probability & the Rules of Probability

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

- Calculate conditional probability
- Conditional probability and independence
- Conditional probability and independence
- Conditional probability tree diagram example
- Conditional probability using two-way tables
- Conditional probability with Bayes' Theorem
- Dependent probability
- Tree diagrams and conditional probability
- Trends in categorical data

Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.

Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

- Conditional probability tree diagram example
- Dependent probability introduction
- General multiplication rule example: dependent events
- General multiplication rule example: independent events
- Interpret probabilities of compound events
- Interpreting general multiplication rule
- Probability with general multiplication rule
- Tree diagrams and conditional probability

Use permutations and combinations to compute probabilities of compound events and solve problems.

- Combination example: 9 card hands
- Combination formula
- Combinations
- Example: Different ways to pick officers
- Example: Lottery probability
- Factorial and counting seat arrangements
- Handshaking combinations
- Intro to combinations
- Mega millions jackpot probability
- Permutation formula
- Permutations
- Permutations & combinations
- Possible three letter words
- Probability using combinations
- Probability with combinations example: choosing cards
- Probability with combinations example: choosing groups
- Probability with permutations & combinations example: taste testing
- Probability with permutations and combinations
- Ways to arrange colors
- Ways to pick officers
- Zero factorial or 0!