4.A pharmaceutical company has 40 manufacturing sites in their network. Microbial contamination at any one site is a significant concern from the perspectives of health and safety, potential lost sales, and significant remediation costs. Historically, the chance of microbial contamination for a site is about 5% per year. The remediation costs for a single contamination is about $35 million. The CFO states that a material consequence to the company would be three or more microbial contaminations across the manufacturing network in a given year.

a) What is the annual probability of having three or more microbial contaminations across the manufacturing network?

b) Given three or more microbial contaminations have occurred, what are the 10th, 50th, and 90th percentiles of remediation costs to the company?