Keystone puts a lot of work into showcasing properties to potential buyers (something like a personal open house). Each showcase results in either a ‘success’ (the buyer purchases the property) or a ‘failure’ (the buyer refuses to buy the property). Historically, Keystone figures that on any given showcase there is an 18% chance they will be successful and make a sale. Keystone has 8 showcases planned for this month, and they would like to explore some probabilities surrounding these showcases to help them manage this process and forecast revenues. In particular, Keystone wants to see at least two of these showcases turn into sales. What are the chances that exactly 1 of the showcases will result in a sale? What are the chances that they will make at least 3 sales? What are the chances that they will make fewer than 2 sales? Sometimes buyers will request a second viewing of the property. Based on historical evidence, buyers ask for a second viewing on 80% of successful showcases and on only 25% of unsuccessful showcases. What are the chances that a showcase will be successful, given that a potential buyer has asked for a second viewing?

What are the chances that at least two of the showcases will result in a sale?

Exactly one of the showcases will result in a sale?

What are the chances that they will make at least three sales?

What are the chances that they will make fewer than two sales?

What are the chances that a showcase will be successful, given that a potential buyer has asked for a second viewing?