Unit 7 - What Do You Expect?

By the end of this unit, students are expected to:

Experimental and Theoretical Probabilities:

• 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:

• 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

Helping At Home

When your child encounters a new problem, it is a good idea to ask questions such as:

• What are the possible outcomes for the event(s) in this situation?

• Are these outcomes equally likely?

• Is this a fair or unfair situation?

• Can I compute the theoretical probabilities or do I conduct an experiment?

• How can I determine the probability of one event followed by a second event: two-stage probabilities?

• How can I use expected value to help me make decisions?

What Do You Expect? - Explanation of Concepts for Those Helping at Home - Connected Mathematics 3 Resource