All Questions
Tagged with paradoxes probability-theory
23
questions
4
votes
2
answers
90
views
Question Regarding Proposed Solution to the (Closed Envelope Version of) Two Envelope Paradox
Su, Francis, et. al. have a short description of the paradox here: https://www.math.hmc.edu/funfacts/ffiles/20001.6-8.shtml
I used that link because it concisely sets forth the paradox both in the ...
- 413
1
vote
1
answer
314
views
Conditions required to yield exactly one solution in Bertrand's Paradox
Introduction: Bertrand's Paradox
Given two concentric circles ($S_1$, $S_2$) with radii $R_1=r$ and $R_2=\frac{r}2$, what is the probability, upon choosing a chord $c$ of the circle $S_1$ at random,...
- 532
0
votes
0
answers
112
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A paradox with the additivity axiom of probability theory
Suppose F is a finite set of propositions such that, for every proposition A in F and every proposition B in F such that A is distinct from B, P(A) = P(B) and A is inconsistent with B.
By using the ...
- 91
10
votes
1
answer
975
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How to show that the event that a prisoner does not go free is not measurable
I was reading this webpage a few months ago about the following problem-
A countable infinite number of prisoners are placed on the natural numbers, facing in the positive direction (ie, everyone can ...
- 35.1k
1
vote
2
answers
3k
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resolving expected utility of st. petersburg paradox with logarithmic utility
St. Petersburg paradox is a game where you toss a fair coin repeatedly and if it lands heads on the $k$th trial you get $2^n$ dollars. Expected utility of game is:
$E(U) = \sum_{k=1}^{\infty}[0.5*0 + ...
- 355
6
votes
2
answers
514
views
Formal approach to (countable) prisoners and hats problem.
I've found this nice puzzle about AC (I'm referring to the countable infinite case, with two colors). The puzzle has been discussed before on math.SE, but I can't find any description of what is ...
- 1,142
6
votes
1
answer
4k
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Expected value of the distance between 2 uniformly distributed points on circle
I have the following problem (related to Bertrand):
Given a circle of radius $a=1$. Choose 2 points randomly on the circle circumference.
Then connect these points using a line with length $b$. ...
- 63
30
votes
7
answers
5k
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Card doubling paradox
Suppose there are two face down cards each with a positive real number and with one twice the other. Each card has value equal to its number. You are given one of the cards (with value $x$) and after ...
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