The manager of a small business receives a shipment of five hard drives. Three hard drives are good and 2 are defective. If a computer repair shop purchases 3 of this stock of hard drives from the small business and the selection was made at random.
1. List the elements of the sample space S using the letters G and D for good and defective respectively.
2. If x represents the number of defective hard drives in a random sample of three hard drives, list in the form of a table, the values of x for each point in the sample space S and the corresponding frequencies.
3. What is the probability that the repair shop purchased at least 1 defective hard drive?
4. What is the probability the repair shop purchased more than 2 defective hard drives?
5. What is the mean number of defective hard drives that the small business receives if all their shipments come in sets of five that contain the same proportion of defective hard drives?