The Monty Hall Problem. The DOORs contain two GOATs and a CAR. You select one. The HOST shows you a door with a goat. Do you switch? Answer: Yes, switch. It raises your probability of getting the car from 1/3 to 2/3.
it becomes more intuitive the more doors you add. thinking of it in the framework of 99 goat doors and 1 car door: after you make your selection the host reveals 98 goats, it’s quite obvious you should switch to the one door he didn’t open. It’s only a 1/100 chance your initial selection was the car!
In the game you are given three doors to choose from, two have goats behind them and one has a car. You pick one and then the host reveals a goat behind one of the other doors and asks you if you want to stick with your current choice or swap to the other door. The easiest way to think about the optimal strategy is to realize that because the host will always reveal a goat, switching means you will be guaranteed to change items. If you originally picked a goat then you will switch to a car and if you originally picked a car you will switch to a goat. Since you had a 2/3rds chance of picking a goat you should always pick to switch doors and now you have a 2/3rds chance of getting a car.
I think the easiest way to explain the problem is saying that you are more likely to pick a goat at first, because there are 2 out of 3. When the host removes the other goat, you should switch to take advantage of the initial probability of having picked a goat.
Connections Puzzle #579 🟩🟨🟩🟩 🟩🟨🟩🟩 🟩🟨🟩🟩 🟩🟩🟩🟩 🟨🟨🟨🟨 🟦🟦🟦🟦 🟪🟪🟪🟪 JUST SETTLE NECESSARY FOR COMPLETION INGREDIENTS OF ALCOHOLIC DRINK WITH "S" A MUSICAL GROUP * * My purple category classification is equally correct, so I'm taking it. I made my 3 errors trying to sort the green. Once again, the 2 supposedly easiest categories were the most difficult. Thanks for your explanation of the probability problem!! Even though I have seen this show (You make me feel very old that this was "before your time.") I had never heard of the Monty Hall Probability Problem until today. Your range of knowledge continues to blow me away. Not only could you explain the problem, you knew the article describing it!! Plus you knew that the "alcoholic drink" was an Old Fashioned. Cheers!! ❤😊
So you are on a game show. The host shows you three doors and tells you that behind one door is a car and behind the other two doors are goats. The host asks you to pick a door. Once you've picked your door, the host will open one of the doors that you did not pick that contains a goat. The host gives you the option to switch your choice to one of the two remaining doors. The solution is counter intuitive but your odds are greater if you switch doors.
I'm kinda surprised Chris didn't see Monty Hall immediately when left with those four words. I guess I'm just more familiar with it because of math (and how many times I had to explain it to different friends). (Not surprised not to see it with other answers, though)
The Monty Hall problem is a classic. There are two goats; one always lies and one always tells the truth. The goats can’t be in the same room at the same time. You have to cross the river to an island where Monty Hall is waiting with your door. Then one of the goats says, “I can’t operate on this man, he’s my son!”. How can this be? (Women can’t be doctors).
As someone who is familiar with the maths behind the Monty Hall Problem, your explanation didn't quite make sense to me. But you are correct that the strategy of switching the doors (after the host's reveal) will lead you to the car 2/3 of the time, so it is better to switch (as you say, it initially feels unintuitive, and has led to countless debates). One way to look at it is with your initial choice there is 1/3 chance the car is behind it and 2/3 chance the car is behind one of the other doors. When the host opens one of those other doors (with a goat), there is still a 2/3 chance that the car is behind one of the other doors, and if it is there it must be that door that no-one has yet picked. So switch!
I was going to guess the yellow category first and correctly, but I second guessed myself: Connections Puzzle #579 🟩🟨🟩🟩 -REST- 🟦🟦🟦🟦Ingredients to a mixed drink that I couldn't remember the name of and never had one, but it does sound delicious. 🟨🟨🟨🟨Contingent 🟪🟪🟪🟪Elements of the Monty Hall Experiment, (Let's Make a Deal) 🟩🟩🟩🟩Ways of saying "Calm Down/Simmer Down"
The Monty Hall Problem. The DOORs contain two GOATs and a CAR. You select one. The HOST shows you a door with a goat. Do you switch? Answer: Yes, switch. It raises your probability of getting the car from 1/3 to 2/3.
When I first read the answer to purple I thought it said the "Monty Python problem" 😂 I mean, it does sound like it could be one of their skits.
Funny, I did this, as well. Great minds...LOL
That thumbnail! 😂
it becomes more intuitive the more doors you add. thinking of it in the framework of 99 goat doors and 1 car door: after you make your selection the host reveals 98 goats, it’s quite obvious you should switch to the one door he didn’t open. It’s only a 1/100 chance your initial selection was the car!
I got the purple second- the moment I saw "car" and "goat", my mind immediately jumped to Monty Hall
I spent a long time just staring at the words...then it just kinda came together.
In the game you are given three doors to choose from, two have goats behind them and one has a car. You pick one and then the host reveals a goat behind one of the other doors and asks you if you want to stick with your current choice or swap to the other door. The easiest way to think about the optimal strategy is to realize that because the host will always reveal a goat, switching means you will be guaranteed to change items. If you originally picked a goat then you will switch to a car and if you originally picked a car you will switch to a goat. Since you had a 2/3rds chance of picking a goat you should always pick to switch doors and now you have a 2/3rds chance of getting a car.
I think the easiest way to explain the problem is saying that you are more likely to pick a goat at first, because there are 2 out of 3. When the host removes the other goat, you should switch to take advantage of the initial probability of having picked a goat.
Ahhh, Thanks, I finally get the reasoning. Math was never really my strong suit. 😊
I'm well familiar with the monty hall problem but still couldn't see the connection in this puzzle :\
That explanation 😂
minus the number you first thought of... 😊
Great thumbnail
Connections
Puzzle #579
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🟨🟨🟨🟨
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JUST SETTLE
NECESSARY FOR COMPLETION
INGREDIENTS OF ALCOHOLIC DRINK
WITH "S" A MUSICAL GROUP *
* My purple category classification is equally correct, so I'm taking it. I made my 3 errors trying to sort the green. Once again, the 2 supposedly easiest categories were the most difficult.
Thanks for your explanation of the probability problem!! Even though I have seen this show (You make me feel very old that this was "before your time.") I had never heard of the Monty Hall Probability Problem until today. Your range of knowledge continues to blow me away. Not only could you explain the problem, you knew the article describing it!! Plus you knew that the "alcoholic drink" was an Old Fashioned. Cheers!! ❤😊
So you are on a game show. The host shows you three doors and tells you that behind one door is a car and behind the other two doors are goats. The host asks you to pick a door. Once you've picked your door, the host will open one of the doors that you did not pick that contains a goat.
The host gives you the option to switch your choice to one of the two remaining doors. The solution is counter intuitive but your odds are greater if you switch doors.
I'm kinda surprised Chris didn't see Monty Hall immediately when left with those four words. I guess I'm just more familiar with it because of math (and how many times I had to explain it to different friends).
(Not surprised not to see it with other answers, though)
You have a 67% chance of winning the car by switching, not 50%
Whoops, thank you!
The Monty Hall problem is a classic. There are two goats; one always lies and one always tells the truth. The goats can’t be in the same room at the same time. You have to cross the river to an island where Monty Hall is waiting with your door. Then one of the goats says, “I can’t operate on this man, he’s my son!”. How can this be? (Women can’t be doctors).
horse's name was friday
@Paraninja Ohh, thanks; now I understand. 😂🤣😂🤣😂
As someone who is familiar with the maths behind the Monty Hall Problem, your explanation didn't quite make sense to me. But you are correct that the strategy of switching the doors (after the host's reveal) will lead you to the car 2/3 of the time, so it is better to switch (as you say, it initially feels unintuitive, and has led to countless debates). One way to look at it is with your initial choice there is 1/3 chance the car is behind it and 2/3 chance the car is behind one of the other doors. When the host opens one of those other doors (with a goat), there is still a 2/3 chance that the car is behind one of the other doors, and if it is there it must be that door that no-one has yet picked. So switch!
I was going to guess the yellow category first and correctly, but I second guessed myself:
Connections
Puzzle #579
🟩🟨🟩🟩 -REST-
🟦🟦🟦🟦Ingredients to a mixed drink that I couldn't remember the name of and never had one, but it does sound delicious.
🟨🟨🟨🟨Contingent
🟪🟪🟪🟪Elements of the Monty Hall Experiment, (Let's Make a Deal)
🟩🟩🟩🟩Ways of saying "Calm Down/Simmer Down"