SOLUTION: 3. The four floodgates of a small hydroelectric dam fail and repaired independently of each other. It is known that each floodgate is out of order 4% of the time. What is the proba

Question 1103877: 3. The four floodgates of a small hydroelectric dam fail and repaired independently of each other. It is known that each floodgate is out of order 4% of the time. What is the probability that floodgate 2&3 are out of order provided that floodgate 1 is also out of order. Also, during a tour of the dam, you are told that the chance of all four floodgates to be out of order is 0.0005. Verify whether this statement is true or false.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
If there is a probability of a floodgate's failing of 0.04, and they are independent,the probability of all 4 failing is 0.04^4=2.56 x 10^(-6), which is less than 0.0005.
The wording for the first part of the question is not clear. If 1 is out of order, it doesn't affect 2 and 3, and their joint probability of being out of order is 0.04^2=0.0016. The probability the three are out of order is 0.04^3=0.000064.
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