On the game show "Let's make a deal", Monty Hall (the host) walks up to a contestant and gives them $100 unless they want to play "the three doors". They usually turn down the money and play "the three doors". Now behind one of the doors is an enourmous cash prize, behind the other too are silly prizes such as a years supply of toilet paper or a goat. So Monty asks this same contestant to pick a door, which they do. Then, before opening the chosen door and revealing what's behind it, he opens one of the other doors which reveals one of the lesser prizes. Monty then gives this contestant the option of staying with their chosen door or switching to the other door which still remains closed. The contestant then decides what to do and is rewarded with whatever prize is behind the door they finally chose. So the question is, should the contestant switch or stay?
switching loses if and only if the player initially picks the car, which happens with probability 1/3, so switching must win with probability 2/3.Thus the contestant should switch
ReplyDeleteYou should switch doors.
ReplyDeleteThere are 3 possibilities for the first door you picked:
You picked the first wrong door - so if you switch, you win
You picked the other wrong door - again, if you switch, you win
You picked the correct door - if you switch, you lose
Each of these cases are equally likely. So if you switch, there is a 2/3 chance that you will win (because there is a 2/3 chance that you are in one of the first two cases listed above), and a 1/3 chance you'll lose. So switching is a good idea.