Can you give me an example of probability paradoxes?

Question

Eg The Monty Hall problem.

Answer 1

not off the top of my head..no

Answer 2

Berkson's paradox:
a complicating factor arising in statistical tests of proportions

Bertrand's paradox (probability):
Different common-sense definitions of randomness give quite different results.

Birthday paradox:
What is the chance that two people in a room have the same birthday?

Borel's paradox:
Conditional probability density functions are not invariant under coordinate transformations.

Boy or Girl:
If in a two-child family, one child is a boy, what is the probability that the other child is a girl?

Hodgson's paradox:
the ratio of two Gaussian random variables, both with equal mean, has neither mean nor variance.

Monty Hall problem:
An unintuitive consequence of conditional probability. Essentially the same as the Three Prisoners Problem.

Simpson's paradox:
An association in sub-populations may be reversed in the population. It appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis.

Sleeping Beauty problem:
A probability problem that can be correctly answered as one half or one third depending on how the question is approached.

Three cards problem:
When pulling a random card, how do you determine the color of the underside.

Two-envelope paradox:
You are given two indistinguishable envelopes and you are told one contains twice as much money as the other. You may open one envelope, examine its contents, and then, without opening the other, choose which envelope to take.

Answer 3

Three cards are in a hat. One card is white on both sides; the second is white on one side and red on the other; the third is red on both sides. The dealer shuffles the cards, takes one out and places it flat on the table. The side showing is red. The dealer now says, "Obviously this is not the white-white card. It must be either the red-white card or the red-red card. I will bet even money that the other side is red." Is this a fair bet?