Suppose there are infinite prisoners. Each prisoner wears a red or a blue hat. Every prisoner can see every other prisoner's hats. No prisoners know their hat color. Each prisoner can either attempt to guess his hat color or abstain from guessing. However, in order for the prisoners to succeed, an infinite number of prisoners should make a guess and all the prisoners who guess should guess their hat color right. Can the prisoners come up with a strategy that will enable them to succeed with a probability of at least 0.5?
- via Quora