Probability Reasoning
Georgia Standard: 7.PR.6: Using mathematical reasoning, investigate chance processes and develop, evaluate, and use probability models to find probabilities of simple events presented in authentic situations.
Expectations
Represent the probability of a chance event as a number between 0 and 1 that expresses the likelihood of the event occurring. Describe that a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Approximate the probability of a chance event by collecting data on an event and observing its long-run relative frequency will approach the theoretical probability.
Develop a probability model and use it to find probabilities of simple events. Compare experimental and theoretical probabilities of events. If the probabilities are not close, explain possible sources of the discrepancy.
Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events.
If a student is selected at random from a class, find the probability a student with long hair will be selected.
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
Use appropriate graphical displays and numerical summaries from data distributions with categorical or quantitative (numerical) variables as probability models to draw informal inferences about two samples or populations.
Examples
When rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Kim calculates the probability of landing on heads when tossing a coin to be 50%. She uses this to predict that when Tiffany tosses a coin 20 times, the coin will land on heads 10 times. When Tiffany performed the experiment, the coin landed on heads 7 times. Explain possible reasons why Kim’s prediction and Tiffany’s results do not match.
Find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
Compare the heights of the basketball and the tennis teams. Basketball team’s heights (in inches): 72, 75, 76, 76, 79, 79, 80, 80, 81, 81, 81
Tennis team’s height (in inches): 67, 67, 68, 70, 70, 71, 72, 75, 76, 76, 77
1) How much taller is the basketball team than the tennis team? 2) Two students are trying out for the basketball team. What is the probability their height will be greater than 79 inches?