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