166 Simulating the Probability of Rolling a 3 or 4 3.3 ACTIVITY APPLET You can find the interactive applet for this activity at MyLab Statistics. 166 CHAPTER 3 Probability The Simulating the probability of rolling a 3 or 4 applet allows you to investigate the probability of rolling a 3 or a 4 on a fair die. When the 1 roll or 5 rolls buttons are clicked, the results of the corresponding number of simulated die rolls are added to the Rolls column. Clicking the 1000 rolls button will add the results of the 1000 rolls as fast as possible by skipping the animation. The cumulative results of the rolls are given in the plot showing the cumulative proportion of times a 3 or 4 was rolled versus the total number of rolls. The tallied results are also stored in the table above the graph. The green line in the plot reflects the true probability of rolling a 3 or 4, which is 1/3 ≈ 0.333333. As the virtual die is rolled more and more times, the cumulative proportion of times a 3 or 4 is rolled should converge to this value. Roll # 2 0 1 8 6 4 10 0.8 0.6 0.4 0.2 Rolling a 3 or a 4 1 roll 5 rolls 1000 rolls Outcomes Reset Rolls Event 3 or 4 Proportion of “3 or 4” Convergence Count Total Proportion EXPLORE Step 1 Click 1 roll eight times. Click Outcomes. Click Convergence. Step 2 Click Reset. Step 3 Click 5 rolls four times. Click Reset. Step 4 Click 1000 rolls four times. DRAW CONCLUSIONS 1. Run a simulation of 1 roll, a simulation of 5 rolls, and a simulation of 1000 rolls. Clear the results after each simulation. Compare the cumulative proportion of “3 or 4” for each trial with the theoretical probability of rolling a 3 or 4. 2. You reprogram the applet to find the probability of rolling a number less than 4. How should you change the green line? APPLET
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