2
votes
1answer
55 views

St. Petersburg and the law of large numbers

Recently I learned about the discussion around the St. Petersburg paradox and how people try to explain why the calculated expected value differs so much from most people's intuition. My question: ...
-1
votes
2answers
97 views

Does this paradox have a name?

As a student many years ago I learned of a paradox of something that is almost a certainty, while at the same time being highly improbable. For example, if you flip 10 coins the chances of all being ...
0
votes
2answers
95 views

Could the birthday paradox be interpreted also about deaths?

Is the probability from the birthday paradox also true about deaths? If so, why? Or why not? I would think that it is also true about deaths, but it doesn't say so.
1
vote
2answers
109 views

Explain the Birthday Paradox

this is my first question at Maths Stackexchange, so, first of all, hello world! My question is, I recently read about the Birthday Paradox which states that in a group of 23 people, there's a ...
0
votes
0answers
54 views

World cup birthday paradox for two pairs

The BBC report on the world cup squads The birthday paradox at the World Cup shows the 50:50 prediction for there being 16 teams out of the 32 that meet the pair birthday criteria. However my ...
1
vote
0answers
61 views

Buffon needle in higher dimensions

Imagine a stick of length 1, and also a floor with evenly spaced lines, such that the distance between neighboring lines is also 1. If one throws the stick on the floor, there will be certain ...
1
vote
0answers
79 views

Bus arrival poisson paradox

I have a question about the waiting time paradox for poisson processes(in this case in terms of bus arrivals). Suppose I know that buses arrive with poisson distribution(lambda). I arrive at fixed ...
16
votes
1answer
7k 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), ...
2
votes
1answer
435 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
285 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
166 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
349 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
371 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
262 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
198 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
1answer
139 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 $1/2^n$, ...
8
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
814 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
223 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
601 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
265 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
90 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. ...