### GIGAMIND

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113 Math

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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.

##### Tags:

- statistics
- probabilities