Press 1 to run mode 1. Press 2 to run mode 2.
This is based on a couple of probability tricks with similar results. Mode 1: A bag contains 3 coins: one is heads on both sides, one is tails on both sides, and one has one heads side and one tails side. One of these coins is picked at random and flipped. If the result is heads, what is the probability that the other side of the coin is also heads? Mode 2: You are playing a game show. There are 3 doors. One of them has a cash prize behind them (the program does this at random). You are first asked to pick a door (the program also does this part at random). Before yours is opened, one of the doors without a cash prize behind it is opened (again chosen at random in the simulator program). You are asked if you would like to stay with your door or switch to the other one which is still closed. What is the probability that if you switch to the other remaining door, there will be a cash prize? Both of these seem very much like the probability would be 50-50, but you actually have a 2/3 chance in both cases. Don't believe me? I built a simulator to try each experiment 100,000 times.
