17
votes
8answers
4k views

Is Lewis Carroll's reasoning correct?

A bag contains 2 counters, as to which nothing is known except that each is either black or white. Ascertain their colours without taking them out of the bag. Carroll's solution: One is black, and ...
1
vote
1answer
41 views

Geometrically distributed RV's - what's wrong with my reasoning?

Let $X$ and $Y$ be iid random variables distributed geometrically with probability of success $p$ and support $\mathbb{N}=\{0,1,2,\cdots\}.$ So in particular, letting $q=1-p$, we have that ...
4
votes
5answers
417 views

Coin Flip Betting System

-Read comments before posting I came up with a betting system that seems to defy logic... explain why its wrong? Here's the "logic" behind it Rule: If you flip a coin enough times(x) the number of ...
0
votes
1answer
79 views

Is the conclusion(last line) correct? If not, what's wrong with this proof ? (Probability Density Estimation, Bayesian inference)

(Probability Density Estimation, Bayesian inference) $x_1$ and $x_2$ are independent random variables, so $p\left(x_1,x_2\right)=p\left(x_1\right)\cdot p\left(x_2\right)$ and ...
1
vote
5answers
562 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 ...
7
votes
5answers
598 views

What is the problem in this solution to the Two Child Problem?

The Two Child Problem states In a family with two children, what are the chances, if at least one of the children is a girl, that both children are girls? It is well attested that the answer ...
1
vote
1answer
98 views

Question about Mutual Information

I am learning about mutual information, and am confused about one of the definitions. Mutual information is defined as $ I(X;Y) = H(X) - H(X | Y) $ where, $$ H(X) = \sum_{x} p(x) \log ...