The McThomas School currently has three parking garages, each containing 150 spaces. There are six hundred faculty members in total, and two hundred faculty members have been assigned to each garage. On a peak day, an average of 70% of all Garage A parking permit holders show up, an average of 60% of all Garage B parking permit holders show up, and an average of 75% of all Garage C parking permit holders show up. Suppose the number of people who show up at the three garages are independent. A. How would you model the number of faculty members actually show up in Garage A? (Hint: make an analogy with coin flipping problem.)
B. Consider the case that each person can park only in the assigned garage (no pooling). What is the probability of at least one person not finding a space?
C. Consider the case that each person can park in any of the garage (pooling).