Every 9 weeks, Mr. Millar collects students’ notebooks and checks their homework. He randomly selects 4 different assignments to inspect for all of the students. Marino is one of the students in Mr. Millar’s class. Marino completed 20 homework assignments and did not complete 10 assignments. He is surprised when Mr. Millar only selects 1 assignment that he completed. Should he be surprised? To find out, we want to design a simulation to estimate the probability that Mr. Millar will randomly select 1 or fewer of the homework assignments that Marino completed.

Get 30 identical slips of paper. Write “N” on 10 of the slips and “C” on the remaining 20 slips. Put the slips into a hat and mix well. Draw 1 slip without looking to represent the first randomly selected homework assignment, and record whether Marino completed it. Put the slip back into the hat, mix again, and draw another slip representing the second randomly selected assignment. Record whether Marino completed this assignment. Repeat this process two more times for the third and fourth randomly selected homework assignments. Record the number out of the 4 randomly selected homework assignments that Marino completed in this trial of the simulation. Perform many trials. Find the proportion of trials in which Mr. Millar randomly selects 1 or fewer of the homework assignments that Marino completed.

Determine whether the simulation design is valid. Justify your answer.