Monty Hall probability problem

• There are 3 curtains. One of them has something fabulous behind it.
• You are asked to choose one to win the prize
• They show you one of the 2 that you didn’t choose
• Then you’re asked if you want to hold fast or switch your choice
• Always switch!

The probabilities

• On the first choice, you have a 1/3 chance of picking right and 2/3 chance of picking wrong. You don’t know if you picked right or wrong at first, but you do know the probability of it.
• They will show one of the two choices you didn’t pick, which leaves two of them.
• Always switch and you have a 2/3 probability of winning.
  • If you picked wrong the first time (2/3 chance) and they showed the other wrong one, you’ll switch to the winner.
  • If you picked right the first time (1/3 chance) and they showed one of the wrong ones you’ll switch to the other wrong one
    • But you only had a 1/3 chance to get the right one in the first place, so the higher probability chance is to always switch.