Statistics in a Modern World 800
Solutions to Exam 3

1. 1-(.46+.20)=.34
2.  
   1. not mutually exclusive: there are some males with ears pierced
   2. not independent: .35(.7)=.245, not the same as .09. Anyway, common sense tells us that having ears pierced is very dependent on gender, with females much more likely to do so.
   3. In M but not P: probability .26; in both M and P: probability .09; in P but not M: probability .61
   4. Either .35+.70-.09=.96 or .26+.09+.61=.96
   5. 1-.96=.04
3.  
   1. (iii) both equally likely
   2. (ii) law of small numbers
   3. (ii) Daniel Kahneman (there was a handout and discussion of his work in lecture)
4. 1/4 * 1/3 = 1/12
5.  
   1. 5/6 * 5/6 * 5/6 = 125/216
   2. 1 - 125/216
6. 0(.1)+1(.4)+2(.2)+3(.2)+4(.1)=1.8
7. (g) pseudo-certainty
8. (a) can be explained by the laws of probability (there are so many "surprising" events possible, that in the long run some of them are bound to occur)
9. (e) over-confidence
10. (c) .97 (we demonstrated in class how likely it is in a large group to have at least two shared birthdays; the other three choices are too small)
11.  
    1. (v) optimism
    2. (i) relative frequency
12. (a) because it is most general
13. (b) representativeness
14. (g) conservatism
15. (b) availability
16. (a) anchoring
17.  
    1. First branch-off is for ill (.01) or healthy (.99); after ill branch-off for pos (.9) or neg (.1); after healthy branch-off for pos (.2) or neg (.8)
    2. .01(.9)=.009
    3. .99(.2)=.198
    4. .009+.198=.207
    5. .009/.207=.043
    6. (d) forgotten base rates

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