Problem Statement  
A redundant storage system can survive a certain number of hard drive failures without losing any data. You are doing some analysis to determine the risk of various numbers of drives failing during one week. Your task is complicated by the fact that the drives in this system have different failure rates. You will be given a double[] containing n elements that describe the probability of each drive failing during a week. Return a double[] containing n + 1 elements, where element i is the probability that exactly i drives will fail during a week. Assume that drive failures are independent events.  
Definition  
 
Notes  
  The returned value must be accurate to within a relative or absolute value of 1E9.  
  If events with probabilities p_{1} and p_{2} are independent, then the probability of both occurring is p_{1}p_{2}.  
Constraints  
  failureProb will contain between 1 and 15 elements, inclusive.  
  Each element of failureProb will be between 0.0 and 1.0, inclusive.  
Examples  
0)  
 
1)  
 
2)  
