You have fifty quarters on the table in front of you. You are blindfolded and cannot discern whether a coin is heads up or tails up by feeling it. You are told that x coins are heads up, where 0 < x < 50. You are asked to separate the coins into two piles in such a way that the number of heads up coins in both piles is the same at the end. You may flip any coin over as many times as you want.
On a game show there are three closed doors – one hides a car and the other two conceal a goat. The contestant selects a door, which remains closed, and the host, knowing where the car is hidden, reveals a goat behind one of the remaining two doors. The contestant is then given the option to switch doors or stay with the one they originally selected. What should the contestant do to have the best chance of winning the car?
The contestant should switch doors, which doubles the chance of winning the car. Initially there is a 2/3 chance of picking a goat, but once the other goat is revealed, switching to remaining door gives the contestant a better chance of winning the car. This is known as the Monty Hall Problem and can be very unintuitive.