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Consider the standard "guess which one of three curtains the prize is behind" scenario. After choosing curtain 1, you're shown that nothing resides behind curtain 2. If allowed, would you switch to curtain 3?
Originally posted by chroot
Of course!
- Warren
Originally posted by STAii
1-Mathematically:
The chance of getting the right curtain from the first try is 1/3, after the second curtain is opened the chance of the prize being behin the third curtain will become 2/3, so i would choose the biggest chance.
Originally posted by STAii
2-Trial and error:
Write all the possibilites, you will see that if you change your mind about your curtain decision, you chance of winning will be the double of if you didn't (note that (1/3)*2=2/3 )
I don't see why it wouldn't be 50/50 between the 1st and 3rd.
The Curtain Game, also known as the Monty Hall problem, is a probability puzzle that involves choosing between three curtains, behind which are a prize, a goat, and an empty space. The player makes an initial choice, after which the host reveals one of the other two curtains, always showing a goat. The player is then given the option to switch their choice or stay with their original one.
Many people assume that the chances of winning are equal whether they switch their choice or not, but this is not the case. In fact, the chances of winning increase from 1/3 to 2/3 if the player switches their choice. This can be mathematically proven using conditional probability.
The Curtain Game can be seen as a simplified version of real-life scenarios, such as choosing between different job offers or selecting a door in a game show. The concept of conditional probability and the idea of making strategic choices based on new information can be applied to various situations in real life.
The reason the Curtain Game may seem counterintuitive is because our brains tend to rely on intuition and past experiences when making decisions. In this case, our intuition tells us that the chances of winning remain the same regardless of switching, but the logical and mathematical explanation proves otherwise.
The Curtain Game is a popular example used in the study of probability and decision making. It highlights the importance of understanding conditional probability and making informed choices based on new information. This concept is valuable in various scientific fields, such as statistics, psychology, and economics.