S-MD - Domain

Using Probability to Make Decisions

High School Statistics & Probability · Common Core State Standards · Common Core 2010

Standard Unwrapping

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Vocabulary
expected valuesrandom variableprobability distributionsample spaceprobabilityoutcomesdecisionpayoff valuesgraphdistributionsgame of chancestrategyempirical probabilities
Skills
  • Define (random variable) #dok1
  • Calculate (expected value) #dok1
  • Graph (probability distribution) #dok1
  • Interpret (expected value as mean of probability distribution) #dok2
  • Develop (probability distribution for random variable) #dok2
  • Assign (numerical value to events in sample space) #dok2
  • Evaluate (outcomes using probability) #dok3
  • Compare (strategies based on expected values) #dok3
  • Use (probabilities to make decisions) #dok3
  • Analyze (strategies using probability concepts) #dok4
  • Weigh (possible outcomes of a decision) #dok4
Learning Targets
  • I can define a random variable and assign a numerical value to each event in a sample space. #dok1
  • I can calculate the expected value of a random variable. #dok1
  • I can interpret the expected value as the mean of a probability distribution. #dok2
  • I can develop a probability distribution for a given random variable using both theoretical and empirical probabilities. #dok2
  • I can evaluate outcomes using probability and compare strategies based on expected values. #dok3
  • I can use probabilities to make informed decisions. #dok3
  • I can analyze decisions and strategies using advanced probability concepts, such as weighing possible outcomes of complex decisions. #dok4
Big Ideas
  • Understanding expected values is crucial for making informed decisions using probability.
  • Probability distributions can be developed for various scenarios, aiding in the prediction of outcomes and strategic planning.
Essential Questions
  • What is a random variable and how does it relate to expected values?
  • How can probability distributions be used to predict outcomes?
  • In what ways can expected values guide decision making?
  • What are the differences between theoretical and empirical probability distributions?
  • How can probability concepts be applied to real-world decision-making situations?