Suppose you work for a company that purchases lumber from a major supplier and delivers this lumber to individual clients. Suppo
se that you are able to deliver some of the lumber directly from the supplier to the clients, without ever storing it. Moreover, suppose that the rest of the lumber you deliver to your clients is stored in a company warehouse first, then delivered. Let Pi be the probability that a batch of lumber is infested with termites at the time you purchase it from the above major supplier. Moreover, let Ps be the conditional probability that a batch of lumber will get infested with termites during storage, given that this batch was not infested with termites upon entering storage. Finally, let Po be the probability that a batch of lumber leaving your company’s warehouse is infested with termites. Required:
a. Suppose your company has measured both Po and Ps and wants to compute Pi. Derive an expression for Pi in terms of Ps and Po
b. Suppose your company delivers a batch of lumber to a new client. Suppose half of the lumber you deliver to this client comes straight from your lumber supplier, without ever going to storage, while the other half is delivered from your storage warehouse. Derive an expression for the probability that the lumber you deliver to this client will be infested with termites.
c. Suppose the client in Part (b) discovers that one of the batches of lumber you delivered to them is indeed infested with termites. Derive an expression for the conditional probability, given this infestation, that the infestation occurred as a result of the storage of lumber in your company's warehouse.
