Statistics in a Modern World 800
Solutions to Exam 3

1. 1-(.15+.75)=.1
2.  
   1. no, since probability of both does not equal product of individual probabilities: .05 not equal to (.1)(.3)
   2. no, because there is overlap (.05 were in both categories)
   3. .1+.3-.05=.35
   4. .05/.1=.5
3. (ii) gambler's fallacy
4.  
   1. (i) dependent
   2. 2/4 * 2/3 = 1/3
   3. (b)
5.  
   1. .9 goes with +5 and .1 goes with -200
   2. +5(.9)-200(.1) = -15.5
6.  
   1. 1/2 * 1/2 * 1/2 = 1/8
   2. 1 - 1/8 = 7/8
7. (c) the lowest number of 52 cards come in this category (most specific)
8. (c) the highest number of students come in this category (most general)
9. (d) they must follow the rules of probability, and are often unintuitive
10. (e) optimism
11. (b) (as we discussed in lecture)
12. (a) anchoring
13. (d)
14. (g) conservatism
15. (f) over-confidence
16. (b) availability
17. (f) pseudo-certainty
18. (c) confusion of inverse; and (e) forgotten base rates, but I also accepted (b) availability
19.  
    1. first branch-off: ill or not ill, with probabilities .02 and .98; second branch-off: positive or negative, with probabilities .95 and .05 for those who are ill, .1 and .9 for those who are not ill
    2. .02(.95)=.019
    3. .98(.1)=.098
    4. .019+.098=.117
    5. .019/.117=.16

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