- Understand that probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7-SP5]
- Approximate the probability 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. [7-SP6]
- Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7-SP7]
- Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. [7-SP7a]Example: If a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
- Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. [7-SP7b]Example: Find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open open-end down. Do the outcomes for the spinning penny appear to be equally liked based on the observed frequencies.
- Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7-SP8]
- Understand 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. [7-SP8a]
- Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams.
- For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which composes the event. [7-SP8b]
- Design and use a simulation to generate frequencies for compound events. [7-SP8c]Example: Use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?