Statistics in a Modern World 800
Solutions to Exam 3
- 1-(.46+.20)=.34
-
- not mutually exclusive: there are some males with ears pierced
- 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.
- In M but not P: probability .26; in both M and P: probability .09;
in P but not M: probability .61
- Either .35+.70-.09=.96 or .26+.09+.61=.96
- 1-.96=.04
-
- (iii) both equally likely
- (ii) law of small numbers
- (ii) Daniel Kahneman (there was a handout and discussion of his
work in lecture)
- 1/4 * 1/3 = 1/12
-
- 5/6 * 5/6 * 5/6 = 125/216
- 1 - 125/216
- 0(.1)+1(.4)+2(.2)+3(.2)+4(.1)=1.8
- (g) pseudo-certainty
- (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)
- (e) over-confidence
- (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)
-
- (v) optimism
- (i) relative frequency
- (a) because it is most general
- (b) representativeness
- (g) conservatism
- (b) availability
- (a) anchoring
-
- 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)
- .01(.9)=.009
- .99(.2)=.198
- .009+.198=.207
- .009/.207=.043
- (d) forgotten base rates
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