CISC 7700X Midterm Exam

1. a
2. b
3. c
4. d
5. a
6. b
7. c
8. d
9. a
10. e
11. 9/13
   %P(rain|umbrella) = P(umbrella|rain)*P(rain) / ( P(umbrella|rain)*P(rain) + P(umbrella|-rain)*P(-rain))
   %P(rain|umbrella) = 0.9*0.2 / ( 0.9 *0.2 + 0.1*0.8 )
   %P(rain|umbrella) = 9/10*1/5 / ( 9/10 *1/5 + 1/10*4/5 )
   %P(rain|umbrella) = 9/50 / ( 9/50 + 4/50 ) = 9/50 / 13/50 = 9/50 * 50/13 = 9/13 = 0.69231
12. Not enough data.

13. 81/85
   %P(rain|jacket) =P(jacket|rain)*P(rain)  / ( P(jacket|rain)*P(rain) + P(jacket|-rain)*P(-rain))
   % using: P(rain) = 9/13
   %P(rain|jacket) = (9/10) * (9/13) / ((9/10) * (9/13) + (1/10) * (4/13))
   %P(rain|jacket) = 81/85

14. 0.9

15. 0.94737
   % P(C|RSV)P(RSV) / (P(C|RSV)P(RSV) + P(C|-RSV)P(-RSV))
   %  (0.8 * 0.9)  / ((0.8 * 0.9) + (0.4 * 0.1))  = 0.94737

16. 0.95294
   % P(RSV|F) = P(F|RSV)P(RSV) / (P(F|RSV)P(RSV) + P(F|-RSV)P(-RSV))
   % (0.9 * 0.9) / ((0.9 * 0.9) +   (0.4 * 0.1)  )  = 0.95294

17. Not enough data. 
   % P(RSV|fever, caugh), etc., we don't have P(fever, cough|RSV), etc.

18. 0.97590
   % P(RSV | fever, cough) = P(fever, cough|SRV)P(RSV) / ( P(fever, cough|SRV)P(RSV) + P(fever, cough|SRV)P(RSV)) 
   % P(RSV|C) = P(C|RSV)P(RSV) / ( P(C|RSV)P(RSV) + P(C|-RSV)P(-RSV))  

   % we already have P(RSV|F), so replace that in...
   %  P(RSV|C) = P(C|RSV)P(RSV|F) / ( P(C|RSV)P(RSV|F) + P(C|-RSV)P(-RSV|F)) 
   %           = (0.8 * 0.95294) / ( (0.8 * 0.95294) + (0.4 * (1-0.95294)) ) = 0.97590

   % other way: first cough then fever.
   %  P(RSV|F) = P(F|RSV)P(RSV) / ( P(F|RSV)P(RSV) + P(F|-RSV)P(-RSV)) 
   % we already have P(RSV|C), so replace that in...
   %  P(RSV|F) = P(F|RSV)P(RSV|C) / ( P(F|RSV)P(RSV|C) + P(F|-RSV)P(-RSV|C)) 
   %           = (0.9 * 0.94737) / ( (0.9 * 0.94737) + (0.4 * (1-0.94737)) ) = 0.97590

19. b
20. c