The first year you obtain your Professional Engineer seal, you design and observe construction of small dams, each of which is in a different area of the country. Each of these dams is designed to pass the 200-year storm without overtopping, since they are relatively small and no loss of life or damage to property is likely if they do fail. After that first year, you never design another dam for the rest of your career since you move into management.
a. What is the probability that the very first dam you designed will overtop during your anticipated 35-year career?
b. What is the probability that one or more of the first 4 dams you designed will be overtopped during your career?
c. What is the probability that all 4 dams will overtop during your career?