113 Math
113.038.02 Probability - Monty Hall probability problem

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.

  • statistics
  • probabilities