U8 Probability and Combinatorics(KA/PRE/U8)

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Unit 8: Probability and Combinatorics

Venn Diagrams and the Addition Rule

Venn Diagrams help us see how different groups overlap. Addition Rule: If A and B are two events, then: P(A or B) = P(A) + P(B) - P(A and B)

Multiplication Rule for Probabilities

If two events are independent, P(A and B) = P(A) × P(B).

Permutations

Permutations = number of ways to arrange things in order. Example: How many ways can 3 toys be arranged on a shelf?

Combinations

Combinations = number of ways to choose things when order does NOT matter. Example: How many ways to pick 2 toys from 5?

Probability Using Combinatorics

Use combinations to count outcomes and calculate probability.

Probability Distributions Introduction

A probability distribution shows all possible outcomes and how likely they are.

Theoretical & Empirical Probability Distributions

Theoretical = based on math Empirical = based on experiments (real data)

Decisions with Probability

We can make smart choices by comparing probabilities of outcomes!

Expected Value

Expected value = the average result you expect if you repeat an action many times.

Quiz: Test Your Understanding

If you toss a fair coin, what is the probability of getting heads?

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