What Do You Expect?: Probability and Expected Value
Experimental and Theoretical Probabilities: Explore and learn basic probability concepts and understand that you can build probability models by gathering data from experiments (experimental probability) and by analyzing the possible equally likely outcomes (theoretical probability).
- Recognize that probabilities are useful for predicting what will happen over the long run
- For an event described in everyday language, identify the outcomes in the sample space, which compose the event
- Interpret experimental and theoretical probabilities and the relationship between them and recognize that experimental probabilities are better estimates of theoretical probabilities when they are based on larger numbers
- Distinguish between equally likely and non-equally likely outcomes by collecting data and analyzing experimental probabilities
- Realize that the probability of simple events is the fraction of outcomes in the sample space for which the event occurs
- Recognize that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring
- Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability
- Determine the fairness of a game
Reasoning with Probability: Explore and develop probability models by identifying possible outcomes and analyze probabilities to solve problems.
- Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events
- Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process
- Represent sample spaces for simple and compound events and find probabilities using organized lists, tables, tree diagrams, area models, and simulation
- Realize that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs
- Design and use a simulation to generate frequencies for simple and compound events
- Analyze situations that involve two stages (or two actions)
- Use area models to analyze the theoretical probabilities for two-stage outcomes
- Analyze situations that involve binomial outcomes
- Use probability to calculate the long-term average of a game of chance
- Determine the expected value of a probability situation
- Use probability and expected value to make a decision
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