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