Chapter 1
Numbers and Operations
Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Statistics And Probability
1. Uses counting techniques (e.g., the counting principle, tree diagrams) to answer questions involving a finite sample space
Counting techniques allow us to determine the total number of possible outcomes in a situation, which is the denominator when calculating probabilities.
The fundamental counting principle says that if one action can be performed in m ways and another in n ways, then there are m × n possible combined outcomes. This generalizes: if k independent choices are made, with n₁, n₂, n₃, … nₖ possible outcomes respectively, then the total number of outcomes is n₁ × n₂ × n₃ × … × nₖ.
Example: A password consisting of 3 letters followed by 2 digits. Each letter has 26 possibilities, and each digit has 10 possibilities. By the counting principle, the total number of passwords is 26³ × 10² = 175,760,000.