OGM.13.PRB
Open Global Math Standards 2026™ · 12th Grade
Theoretical & Experimental Probability, Random Variables, and Decision Analysis
Grade12th Grade
SubjectMath
Levelstrand
Child standards (4)
- OGM.13.PRB.1Define sample spaces and compound events using set notation (unions, intersections, complements); apply permutations, combinations, counting principles, and geometric area-based probability models to solve contextual problems.
- OGM.13.PRB.2Apply the Addition Rule $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, conditional probability formula $P(A|B) = \frac{P(A \cap B)}{P(B)}$, and General Multiplication Rule; evaluate event independence ($P(A \cap B) = P(A)P(B)$ and $P(A|B) = P(A)$) with and without replacement using Venn diagrams, tree diagrams, and two-way tables in everyday and technical contexts.
- OGM.13.PRB.3Define discrete random variables $X$; construct probability distributions from theoretical and empirical models; calculate and interpret expected value $E(X) = \sum x P(X = x)$ as the mean of the distribution; select between discrete models (including the Binomial distribution $B(n, p)$) and continuous models based on context.
- OGM.13.PRB.4Apply expected value and probability concepts to analyze decision-making and strategies (games of chance, insurance policies, medical screening, operational optimization, fair decision procedures).