GPS Alignment: Instructor Page
Week 14: Data Analysis - Probability

Roll a pair of die 10 times, recording the sum of the two die at each roll. What is the experimental probability of getting a sum of 7? A sum of 4? A sum of 2? How does this compare to the theoretical probability?

Roll the die 20 more times, recording the sum each time. Consolidate this data with the previous data. What is the experimental probability of getting a sum of 7? A sum of 4? A sum of 2? How does this compare to the theoretical probability?

Use a spreadsheet to simulate a large number of trials or consolidate your data with other students in the class. Construct a distribution graph using the data. How does the number of trials affect the experimental probability?

 GPS As seen in Problem Exploration M6D1:  Students will pose questions, collect data, represent and analyze the data, and interpret results. a. Formulate questions that can be answered by data. Students should collect data by using samples from a larger population (surveys), or by conducting experiments. b. Using data, construct frequency distributions, frequency tables, and graphs. c. Choose appropriate graphs to be consistent with the nature of the data (categorical or numerical). Graphs should include pictographs, histograms, bar graphs, line graphs, circle graphs, and line plots. a. Students will conduct an experiment by using real dice or a simulator (like on TI graphing calculators). b. Students are collecting data as they roll the dice and write down the trial occurrences in a frequency table. c. This data can be displayed using different types of graphs, such as bar and circle graphs. M6D2:   Students will use experimental and simple theoretical probability and will understand the nature of sampling. They will also make predictions from investigations. a. Predict the probability of a given event through trials/simulations (experimental probability), and represent the probability as a ratio. b. Determine, and use a ratio to represent, the theoretical probability of a given event. a. The students have two die (or a simulator like the TI graphing calculator) and can write down trial occurrences and predict probabilities based on these simulations. b. The student can examine the theoretical probability of rolling each number on one die and each sum on two dice. M7D1:  Students will pose questions, collect data, represent and analyze the data, and interpret results. a. Formulate questions and collect data from a census of at least 30 objects and from samples of varying sizes. b. Construct frequency distributions. f. Analyze data using appropriate graphs, including pictographs, histograms, bar graphs, line graphs, circle graphs, and line plots introduced earlier, and using box-and-whisker plots and scatter plots. g. Analyze and draw conclusions about data, including a description of the relationship between two variables. Students are collecting and organizing the data found from the trials of rolling the die. They may enter the data in a spreadsheet or in a graphing program (i.e. GraphMaster) to create graphs. g. Experimental probability is all about experimenting and trying to find the theoretical probability. The graphs will show the experimental probability for that one experiment. The students should understand through discussion that the experimental probability will change each time the experiment is run. Further, the student should understand that by the Law of Larger Numbers, as there are more trials in a given experiment, the experimental probability becomes closer to the theoretical probability. M8D3: Students will use the basic laws of probability. a. Find the probability of simple independent events. b. Find the probability of compound independent events. a. The student should examine the probability of rolling a 1, 2, 3, 4, 5, or 6 on one die and the probability of rolling a sum of 1, 2, 3,…, 11, or 12 with two dice. b. This experiment involves two dice making it a compound experiment. Since the outcome on one die is not related to the outcome on the other die, the experiment is independent. The probability can be found by determining the number of possible outcomes for a given number (1/6*1/6) and the total number of outcomes (36 for this experiment).