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Corruption in my file (Posted on 2019-03-07) Difficulty: 4 of 5
I have a very important file, so I've saved a copy on 10 of my 20 hard-drives. However, N of these hard-drives will be corrupted, where N is equally likely to be 0, 1, 2,..., 20. What is the probability that my file will be safe?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution solution Comment 1 of 1
For n=0 to 9, the file will definitely be safe in at least one of the drives.

If 10 drives are corrupted, the probability that all 10 copies are lost is 10/20 * 9/19 * ... * 1/11.

If 11 drives are corrupted, the probability that all 10 copies are lost is 11/20 * 10/19 * ... * 2/11.

In general if more than 9 drives are corrupted, the probability that all copies are lost is n! / (n-10)! / (20! / 10!)

The overall probability that the file is lost is the sum of these probabilities divided by 21. Then, when that quotient is subtracted from 1, you get the probability the file is safe somewhere on a good hard drive.
 
  n   probability 
      of loss
  
 10   1/184756 
 11   1/16796 
 12   3/8398 
 13   1/646 
 14   7/1292 
 15   21/1292 
 16   14/323 
 17   2/19 
 18   9/38 
 19   1/2 
 20   1 
 
 The total when divided by 21 adds up to an overall probability of loss as 1/11, so the probability the file is safe is 10/11.
 
    5   kill "crptfile.txt":open "crptfile.txt" for output as #2
   10   for N=10 to 20
   20     P=!(N)//!(N-10):P=P*!(10)//!(20)
   21       Tot=Tot+P
   30     print N,P:print #2,N,P
   40   next
   60   print Tot//21:print #2,Tot//21
   70   close #2


  Posted by Charlie on 2019-03-07 13:08:51
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