Statistics in a Modern World 800
Solutions to Exam 3
- 1-(.15+.75)=.1
-
- no, since probability of both does not equal product of individual
probabilities: .05 not equal to (.1)(.3)
- no, because there is overlap (.05 were in both categories)
- .1+.3-.05=.35
- .05/.1=.5
- (ii) gambler's fallacy
-
- (i) dependent
- 2/4 * 2/3 = 1/3
- (b)
-
- .9 goes with +5 and .1 goes with -200
- +5(.9)-200(.1) = -15.5
-
- 1/2 * 1/2 * 1/2 = 1/8
- 1 - 1/8 = 7/8
- (c) the lowest number of 52 cards come in this category (most specific)
- (c) the highest number of students come in this category (most general)
- (d) they must follow the rules of probability, and are often unintuitive
- (e) optimism
- (b) (as we discussed in lecture)
- (a) anchoring
- (d)
- (g) conservatism
- (f) over-confidence
- (b) availability
- (f) pseudo-certainty
- (c) confusion of inverse; and (e) forgotten base rates,
but I also accepted (b) availability
-
- 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
- .02(.95)=.019
- .98(.1)=.098
- .019+.098=.117
- .019/.117=.16
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