ertod 1 (Mo.. Newsela / Instructio.. In Log in / NaRedink. Weviceo 4.23 Out: Simulation and Modeling with Data A disc jockey at a school dance has equal numbers of rock and pop songs that she randomly selects from. She designs a simulation to estimate the probability that the next three songs are all rock songs. Which simulation design could she use to estimate the probability? A. Number cube Let \( 1,2,3,4= \) rock Let 5, \( 6= \) pop Roll cube three times. Repeat. B. Number cube Let even number \( = \) rock Let odd number = pop Roll cube three times. Repeat. C. Random digits Let \( 0,1,2,3= \) rock Let \( 4,5,6,7,8,9= \) pop Select three random digits. Repeat. D. Number cube Let \( 1= \) rock Let \( 2= \) pop Roll cube three times. Repeat.

To estimate the probability that the next three songs are all rock songs, the simulation should ensure that each song selection has an equal probability of being rock or pop. Here's an analysis of each option: **A. Number cube** - **Setup**: Let \(1, 2, 3, 4\) represent rock and \(5, 6\) represent pop. - **Probability**: \(P(\text{rock}) = \frac{4}{6} = \frac{2}{3}\), \(P(\text{pop}) = \frac{2}{6} = \frac{1}{3}\). - **Issue**: This does not maintain equal probabilities for rock and pop songs. **B. Number cube** - **Setup**: Let even numbers represent rock and odd numbers represent pop. - **Probability**: \(P(\text{rock}) = \frac{3}{6} = \frac{1}{2}\), \(P(\text{pop}) = \frac{3}{6} = \frac{1}{2}\). - **Advantage**: This correctly maintains equal probabilities for both rock and pop songs. **C. Random digits** - **Setup**: Let \(0, 1, 2, 3\) represent rock and \(4, 5, 6, 7, 8, 9\) represent pop. - **Probability**: \(P(\text{rock}) = \frac{4}{10} = 0.4\), \(P(\text{pop}) = \frac{6}{10} = 0.6\). - **Issue**: The probabilities are not equal, which does not match the scenario. **D. Number cube** - **Setup**: Let \(1\) represent rock and \(2\) represent pop. - **Issue**: It's unclear how the other numbers (3-6) are handled, potentially leading to unequal probabilities or undefined outcomes. **Conclusion:** Option **B** correctly simulates the scenario by ensuring each song has an equal probability of being rock or pop, making it the best choice for estimating the desired probability. **Answer:** **B. Number cube** Let even number = rock and odd number = pop. Roll cube three times. Repeat.