## Problems that WILL be on your Midterm

### Honor Code: Don't discuss these with anyone else.

You are a real-estate developer, and have been hit hard by the housing crunch. Right now, you have an inventory of 40 (nearly identical) houses which you've built on spec (i.e., with borrowed money).

You currently have 12 prospective purchasers engaged in ongoing negotiations. You feel that five are pretty well hooked - Each has a 75% chance of ultimately buying one of your homes. The other seven you're not so sure about - The chance of each buying a home looks, at this point, to be about 50%. (Their final decisions will be made independently.)

What's the probability that you'll reap at least 8 sales from this group of 12 prospective buyers? (Use a 100,000-observation simulation to estimate this probability, and also report the margin of error in your estimate.)

You're scheduled to show each of 10 prospects a sampling of model homes. From prior experience, you believe that each prospect, independently, will have a 30% chance of leaving after seeing one home, a 50% chance of looking at two homes, and a 20% chance of looking at three different homes. How likely is it that you'll end up showing at least 18 homes? (Use a 100,000-observation simulation to estimate this probability, and also report the margin of error in your estimate.)

You purchase bricks from two different suppliers, placing a single order with one of them each month. Your purchasing agent has been randomly (with equal probabilities) ordering from one or the other each month. Your monthly orders vary normally, with a mean of $90,000 and a standard deviation of $25,000. Each supplier has offered you a luxurious golfing weekend as a reward if you order at least $500,000 in bricks from his/her company over the next year.

What is your probability of winning both dealers' rewards? (Use a 40,000-observation simulation to estimate this probability, and also report the margin of error in your estimate.)

You decide to shoot for the rewards by instructing your agent to order from one supplier every month until the order total reaches or exceeds $500,000, and then to order from the other for the remaining months of the year.

Under this new policy, what is your probability of winning both dealers' rewards? (Use a 40,000-observation simulation to estimate this probability, and also report the margin of error in your estimate.)