Researchers recruited 20 volunteers—8 men and 12 women—to take part in an experiment. They randomly assigned the subjects into two groups of 10 people each. To their surprise, 6 of the 8 men were randomly assigned to the same treatment. Should they be surprised? We want to design a simulation to estimate the probability that a proper random assignment would result in 6 or more of the 8 men ending up in the same group.

Get 20 identical slips of paper. Write “M” on 8 of the slips and “W” on the remaining 12 slips. Put the slips into a hat and mix well. Draw 10 of the slips without looking and place into one pile representing Group 1. Place the other 10 slips in a pile representing Group 2. Record the largest number of men in either of the two groups from this simulated random assignment. Repeat this process many, many times. Find the percent of trials in which 6 or more men ended up in the same group.

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