Statistics in a Modern World 800
Solutions to Exam 3

1.  
   1. .04+.29=.33
   2. 1-.33=.67
2.  
   1. Venn diagram overlap contains .15; in F but not U is .10; in U but not F is .30 (outside the F and U circles is .45)
   2. .10+.15+.30=.55 (Alternatively, .25+.45-.15=.55)
   3. No, the events are not mutually exclusive because there IS overlap: 15% are first year students AND undeclared. (Many students confused being mutually exclusive with being independent.)
   4. .10 are in F but not U
3.  
   1. inadmissible because probabilities can't be more than 100%
   2. ADMISSIBLE (don't be fooled by representativeness and the conjunction fallacy)
   3. inadmissible because probabilities sum to more than 1
   4. inadmissible because probabilities sum to more than 1 (.3+.9=1.2)
   5. inadmissible because probabilities can't be negative
4.  
   1. 2/4 * 2/3 = 4/12 = 1/3
   2. (i) relative frequency
5. 1/6 * 1/6 = 1/36
6. 0(.1)+1(.1)+2(.5)+3(.3)=2
7. 1/2
8. gambler's fallacy
9. (b)
10. (d)
11. (b)
12. (g)
13.  
    1. (v)
    2. (ii)
14. (e)
15. (a)
16. (d)
17. (b)
18. (b)
19. (a)
20.  
    1. Not independent because there is a higher probability of having an undeclared major for 1st year students than for others. (.6 vs. .4)
    2. (.25)(.6) = .15
    3. (.75)(.4) = .30
    4. .15 + .30 = .45
    5. .15/.45 = 1/3 or .33

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