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  1. Path: sparky!uunet!zaphod.mps.ohio-state.edu!darwin.sura.net!jvnc.net!yale.edu!yale!news.wesleyan.edu!eagle.wesleyan.edu!ytakahashi
  2. Newsgroups: sci.math.stat
  3. Subject: Help with a problem...
  4. Message-ID: <1992Oct11.172756.1@eagle.wesleyan.edu>
  5. From: ytakahashi@eagle.wesleyan.edu
  6. Date: 11 Oct 92 17:27:56 EDT
  7. Organization: Wesleyan University
  8. Nntp-Posting-Host: eagle.wesleyan.edu
  9. Lines: 30
  10.  
  11. Perhaps someone can help me out...
  12.  
  13.  
  14.     Three people work to solve a problem independantly with differing
  15. chances of solving it.  Given these probabilities, what is the probability
  16. that the problem is solved?
  17.  
  18.  
  19. Since they are independent, P(AB) = P(A)*P(B)  by definition
  20. I extended this to... P(ABC) = P(A)*P(B)*P(C)
  21.     (I'm not sure if that's legal to do)
  22. P(AUBUC) = P(A)+P(B)+P(C) - P(ABC)   by definition
  23.  
  24. plug in from above yields...
  25. P(AUBUC) = P(A)+P(B)+P(C) - P(A)*P(B)*P(C)
  26.  
  27. Is P(AUBUC) actually what I am looking for?
  28.  
  29. Did I do anything illegal (mathematically speaking) here?
  30.  
  31. If this is right, then the probability of the problem being solved
  32. is nothing more than the addition of the three individual probabilities
  33. minus their product.  Right?
  34.  
  35. Any help is greatly appreciated. 
  36.  
  37.                 - Yuki
  38.  
  39. please followup to this as my mail server has been unreliable.
  40.  
  41.