11
votes
1answer
159 views

Who discovered this number-guessing paradox?

In this math.se post I described in some detail a certain paradox, which I will summarize: $A$ writes two distinct numbers on slips of paper. $B$ selects one of the slips at random (equiprobably), ...
1
vote
1answer
239 views

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 $b$. ...
3
votes
1answer
192 views

On a scale of 1 to 10, how likely is it that this question is using binary? [closed]

I just read this interesting xkcd strip: At first I thought it was funny, but as I got to ruminate a little over it, I was surprised to be unable to find an answer. As Karolis JuodelÄ— pointed out, ...
2
votes
1answer
86 views

Fingerprint match probability

I am trying to use the formula for the birthday paradox as a reference to figure out an equation that represents the probability of a fingerprint match. Here's the equation for probability of a ...
8
votes
4answers
311 views

St. Petersburg Paradox

A fair coin will be tossed until a heads results. You will then be paid $2^{n-1}$ dollars where $n$ equals the number of flips. Now why is the expected pay out infinite? $$ \sum_{n \geq 1} ...
2
votes
1answer
244 views

Sleeping Beauty paradox - fair prior

I've been reading the Sleeping Beauty problem wiki. The contradicting answers, to me, appear to stem from frequentist and Bayesian interpretations: The "thirder" solution refers to a limit in an ...
5
votes
2answers
257 views

Intuition about whether to switch in box problem

I ran across an apparent paradox which I then located in the paper The Box Problem: To Switch or Not to Switch as such: Imagine that you are shown two identical boxes. You know that one of them ...
2
votes
1answer
177 views

Conditional Probability and Division by Zero

Suppose we are picking points uniformly at random from the surface of the Earth. I want to compute the probability that I pick a point in the Western hemisphere, given that I pick a point on the ...
1
vote
0answers
110 views

How do you explain this probability paradox?

Imagine there are two bags of money, and you are allowed to choose one. The probability that one of them contains $10^{n-1}$ dollars and the other contains $10^{n}$ dollars is $1/2^n$, ...
7
votes
7answers
2k views

Boy and Girl paradox [duplicate]

I am trying to understand the boy and girl paradox. The paradox states that if a family has two children and one of them is a boy, then the probability of the other being a girl is 2/3. When you ...
3
votes
1answer
699 views

Statistics: Bertrand's Box Paradox [duplicate]

Possible Duplicate: Probability problem This is the Bertrand's Box Paradox I read about on Wikipedia: Assume there is three boxes: a box containing two gold coins, a boxwith ...
2
votes
2answers
194 views

Probabilistic paradox: Making a scratch in a dice changes the probability?

For dices that we cannot distinguish we have learned in class, that the correct sample space is $\Omega _1 = \{ \{a,b\}|a,b\in \{1,\ldots,6\} \}$, whereas for dices that we can distinguish we have ...
1
vote
5answers
564 views

How to explain this paradox involving coin-tosses?

I do this experiment: I flip fair coin, if it comes heads on first toss I win. If it comes tails, I flip it two times more and if both heads I win. Else, I flip it 3 more times, if it comes heads all ...
35
votes
6answers
2k views

A variant of the Monty Hall problem

Everybody knows the famous Monty Hall problem; way too much ink has been spilled over it already. Let's take it as a given and consider the following variant of the problem that I thought up this ...
4
votes
1answer
231 views

Bertrand's paradox (statistics)

I just learned about Bertrand paradox in today's class, and am very shocked. I was wondering if there are indeed only 3 (known?) unique ways of picking a chord in a circle at random, with 3 different ...
1
vote
0answers
89 views

Paradox of a set being twice as big as another one [duplicate]

Possible Duplicate: Card doubling paradox I don't know how to resolve the following paradoxon: Assume two finite sets A, B, one being twice as big than the other, but you don't know which. ...