Probability I: Introductory Ideas

The four floodgates of a small hydroelectric dam fail and are repaired independently of each other. From experience, it's known that each floodgate is out of order 4 percent of the time.

1. If floodgate 1 is out of order, what is the probability that floodgates 2 and 3 are out of order?
2. During a tour of the dam, you are told that the chances of all four floodgates being out of order are less than 1 in 5,000,000. Is this statement true?

Solution