Explore Conditional Probability with my hands-on activity!
This game is named after Monty Hall who was the original Game Host of the American television game show Let's Make a Deal. In that show, contestants had to choose what was behind one of three hidden doors and had a chance to change their answer after seeing what was behind one of the un-chosen doors. There are no guarantees for any given turn, but if this game is played many times, switching an initial choice is the best strategy! Why? Because the conditional probability of an event is the probability that the event will occur given the knowledge that another event has already occurred. In the Monty Hall problem, once one of the empty cups is eliminated and players see the 2 remaining cups, they usually think there’s a 1 in 2 chance that they have picked correctly. But, in terms of probability, their first choice has a 1 in 3 chance of being correct. After the first cup is eliminated, if a player switches from their first choice, the chances of winning increase to 2 in 3.