The Senior Class sponsor at a high school has enough extra money in the Grad Night budget to pay for meals for 3 of the 9 volunteer faculty members chaperoning the students on the trip. The volunteers are comprised of 6 teachers and 3 paraeducators. The Senior Class Sponsor selects the 3 people who will receive free meal vouchers and states that the people were selected at random. The 3 people selected were all paraeducators. All of the volunteers were curious how no teachers were picked for a free meal voucher if the choice were truly random. (a) Calculate the probability that randomly selecting 3 people from a group of 6 teachers and 3 paraeducators will result in selecting 3 paraeducators.

(b) Based on your answer to part (a), is there reason to doubt the Senior Class Sponsor’s claim that the 3 people were selected at random? Explain.

(c) An alternative to calculating the exact probability is to conduct a simulation to estimate the probability. A proposed simulation process is described below.

Each trial in the simulation consists of rolling three fair, six-sided dice, one die for each of the Grad Night chaperones. For each die, rolling a 1, 2, 3, or 4 represents selecting a teacher; rolling a 5 or 6 represents selecting a paraeducator. After 1,000 trials, the number of times the dice indicate selecting 3 paraeducators is recorded.

Does the proposed process correctly simulate the random selection of 3 paraeducators from a group of 9 people consisting of 6 teachers and 3 paraeducators? Explain why or why not.