CISC 7700X Final Exam 1. c 2. b 3. c 4. d 5. e 6. c 7. b 8. a 9. c 10. 0.027027 or 1/37 or 2.7% given: P(b) = 0.1, P(-b)=0.9, P(-c|b)=0.9, P(c|b)=0.1, P(-c|-b)=0.6, P(c|-b)=0.4 P(b|c) = P(c|b)P(b)/P(c) = P(c|b)P(b)/ (P(c|b)P(b)+P(c|-b)P(-b)) = (0.1*0.1) / ( (0.1*0.1) + (0.4*0.9)) = 0.027027 11. not enough info; we don't have P(c,m|b) given: P(b) = 0.1, P(-b)=0.9, P(-c|b)=0.9, P(c|b)=0.1, P(-c|-b)=0.6, P(c|-b)=0.4, P(m|b) = 0.95, P(-m|b) = 0.05, P(m|-b)=0.3, P(-m|-b)=0.7 P(b|c,m) = P(c,m|b)P(b)/P(c,m) = P(c,m|b)P(b)/ ( P(c,m|b)P(b) + P(c,m|-b)P(-b)) not enough info; we don't have P(c,m|b) and P(c,m) 12. 0.080851 or 19/235 or 8.08% given: P(b) = 0.1, P(-b)=0.9, P(-c|b)=0.9, P(c|b)=0.1, P(-c|-b)=0.6, P(c|-b)=0.4, P(m|b) = 0.95, P(-m|b) = 0.05, P(m|-b)=0.3, P(-m|-b)=0.7 assume: P(c,m|b) = P(c|b)P(m|b), and P(c,m)=P(c)P(m), etc. P(b|c,m) = P(c,m|b)P(b)/P(c,m) = P(c|b)P(m|b)P(b)/(P(c|b)P(m|b)P(b)+P(c|-b)P(m|-b)P(-b)) = (0.1*0.95*0.1) / ( 0.1*0.95*0.1 + 0.4*0.3*0.9 ) = 0.080851 13. c 14. e 15. b 16. b 17. c 18. d 19. d 20. b