William_Kasper

Let's establish some notation first:

P(H): My prior probability that the coin came up heads. Because we're assuming that the coin is fair before you present any evidence, I assume a 50% chance that the coin came up heads.

P(H|E): My posterior probability that the coin came up heads, or the probability that the coin came up heads, given the evidence that you have provided.

P(E|H): The probability of observing what we have, given the coin in question coming up heads.

P(E&H): The probability of you observing the evidence and the coin in question coming up heads.

P(E&-H): The probability of you observing the evidence and the coin in question coming up tails.

P(E): The unconditional probability... (read 450 more words →)

But why is the goal of voting an example important? For me, what matters is creating your own example, and helping those who put theirs.

I agree with you. Receiving votes on our posts and comments is only an instrument to help us build better content. The content and how people use it is what matters.

Although the karma voting system provides imperfect information, it provides cheap imperfect information. Separating the question and answer seems like an easy way to make better use of the information that the votes provide. One benefit that I see from the separation is that you receive slightly more detailed feedback, like in a case where some people might... (read more)

Here's a solution to a more general version of the problem:

Let's say that the red envelope contains N times as much money as the blue envelope with probability p, and the blue envelope contains N times as much money as the red envelope with probability (1 - p).

Without loss of generality, N is at least 1.

If N = 1, both envelopes contain the same amount, and there is no point in switching.

If N > 1, let the variable s represent the smaller amount of money between the amounts of the two envelopes. So one envelope contains s, and the other envelope contains Ns.

Scenario 1: The blue envelope contains s,... (read more)

No, the chance that the kidnapped child is a boy is 1/2.

In the correct version of this story, the mathematician says "I have two children", and you ask, "Is at least one a boy?", and she answers "Yes". Then the probability is 1/3 that they are both boys.

In the correct version of the story, you do not gain access to any information that allows you to differentiate between the mathematician's two children and identify a specific child as a boy.

A woman says, "I have two children." You respond, "What are their sexes?" She says, "At least one of them is a boy. The other was kidnapped before I was informed of