Fun Mathy Type Riddles

[mlmooney89]

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It is because, at first, your chance of hitting the right door is 1/3. So, if you stick with you originally chosen door, you have a 1/3 probability of being right.
When the guy gives you the option to switch, you automagically have 2/3 chance to get the right door.

An equivalent way to see it is to imagine you have 100 doors from where to choose.
You pick one and then the guy opens 98 doors that don't have the prize, leaving your door and another one closed. Should you switch your bet to that other door?
What are the chances that you got the door right on your first attempt? 1/100.
Now that you've been shown that 98 other doors have no prize, is the other door that the guy left closed the one with the prize, or yours?

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But doesn't the ratio start over? Yes it was 1/3 to begin with but then you are sitting there and the first door is open you have a 50/50 chance that the next door will be the car.

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[Edwardo Piet]

I don't know what that means! lol

I swear I have a love hate relationship with this stuff. It drives me crazy and I never get the answer but I love the process. I've tried so just tell me :p

I know there's an advantage to switching because there's a thread about this, but I'll never understand why.

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It is because, at first, your chance of hitting the right door is 1/3. So, if you stick with you originally chosen door, you have a 1/3 probability of being right.
When the guy gives you the option to switch, you automagically have 2/3 chance to get the right door.

An equivalent way to see it is to imagine you have 100 doors from where to choose.
You pick one and then the guy opens 98 doors that don't have the prize, leaving your door and another one closed. Should you switch your bet to that other door?
What are the chances that you got the door right on your first attempt? 1/100.
Now that you've been shown that 98 other doors have no prize, is the other door that the guy left closed the one with the prize, or yours?

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Wait is this the Monty Hall problem? That's my favorite problem ever.

[FatAndFaithless]

Oooh the Monty Hall Problem is a great one.

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The intuitive 'resetting' of the ratios really trips people up since the ratios aren't reset at all. You always have a 2/3 chance to win if you switch doors, and a 1/3 chance to win if you don't switch.

It gets a lot more understandable if you draw it in a table or a picture like this one:


or

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[Edwardo Piet]

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That's it. There's a 1 in 3 chance that the first one you picked is a car.

When a goat is revealed then the chance you picked the car to begin with is still 1 in 3.

What the reveal of the goat means is that by switching you are DEFINITELY not going to switch to the one goat that was already revealed to be wrong. So 2 out of 3 times you will switch to the car and 1 out of 3 times your original pick was the car.

This is the way you have to think about it after the goat has been revealed: "unless this door is the car then switching will DEFINITELY be the car".

It's my favorite problem ever because it's both pure logic and very counterintuitive. I love it when people don't get it. I spent several hours explaining it to my brother once. He understood it in the end but he said he still felt that it was wrong.

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[Whateverist]

Searched the 3 problem on the internet , if you take in consideration that you have unlimited water it is easy.

It can be.  If you want to show how you'd do it, put your solution in hide tags: [hide] at the beginning, and the same at the end, except with a "/" between the "[" and the "h".

[notimportant1234]

You have only two buckets, one holds exactly 4 gallons of water and the other exactly 7 gallons. Neither bucket contains any markings on it. Using just these two buckets how can you bring back exactly 5 gallons of water?

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the problem found on the internet refferes to the capacity pf the buckets beeing 4 and 7, it goes like this.
You fill the 4 gallon bucket than you pour it inthe 7 gallon one , than you fill again the 4 gallon and you pour it in the 7 gallon until it s full leaving you 1 gallon in the 4 gallon bucket, then you spill all the water from the 7 gallon bucket than pour the 1 gallon remained in the 4 gallon bucket in the 7 gallon one , than fill the 4 gallon bucket and pour it in the 7 galon one , and tada 5 gallons .
Your problem is a bit different , because you are saying the bucket holds an amount of water , but the capacity isn t specified.But you can still assume that you have unlimited water , and not knowing the capacity of the bucket isn't a problem because you can use the water trace left on the bucket .

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[mlmooney89]

I'm going to throw a tantrum cause I don't get it.

Is the first door opened and revealing a goat? If so how do you turn around and get 2/3 from two doors? There is one goat left and one car. You can flip a coin and pick one. Please someone explain it to me because the pictures FatAndFaithless posted make it seem like the door stayed shut.

[Edwardo Piet]

I will try my best to explain it:

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When you are shown a goat you know you won't switch to that goat. You are asked if you want to switch the other other door. That other door either is the car or it's the other goat. That's a 1/2 chance. But if you stay on the car you are right 1/3 times because there are two other goats.  So abstractly staying on the car is like allowing yourself to risk getting a third goat but switching is like avoiding that goat.

The way that makes it easiest for me is to think like this: If I stay on the car I will be right 1 in 3 times... but if it's NOT the car (which is 2 out of 3 times) then switching will DEFINITELY be the car.

There's a 1 in 3 chance that the current door is the car. You know one of the doors isn't the car. And you also know that you won't switch to that door. So if the current door is not the car (which is a 2 in 3 chance) then the other door is definitely the car.

I hope some of the things I have said is helpful

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[mlmooney89]

I will try my best to explain it:

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When you are shown a goat you know you won't switch to that goat. You are asked if you want to switch the other other door. That other door either is the car or it's the other goat. That's a 1/2 chance. But if you stay on the car you are right 1/3 times because there are two other goats.  So abstractly staying on the car is like allowing yourself to risk getting a third goat but switching is like avoiding that goat.

The way that makes it easiest for me is to think like this: If I stay on the car I will be right 1 in 3 times... but if it's NOT the car (which is 2 out of 3 times) then switching will DEFINITELY be the car.

There's a 1 in 3 chance that the current door is the car. You know one of the doors isn't the car. And you also know that you won't switch to that door. So if the current door is not the car (which is a 2 in 3 chance) then the other door is definitely the car.

I hope some of the things I have said is helpful

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But I thought we knew we were on a goat... Is the damn door open or closed? lol Are we saying the last third is the option to stay where we are?

[Edwardo Piet]

I will try my best to explain it:

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When you are shown a goat you know you won't switch to that goat. You are asked if you want to switch the other other door. That other door either is the car or it's the other goat. That's a 1/2 chance. But if you stay on the car you are right 1/3 times because there are two other goats.  So abstractly staying on the car is like allowing yourself to risk getting a third goat but switching is like avoiding that goat.

The way that makes it easiest for me is to think like this: If I stay on the car I will be right 1 in 3 times... but if it's NOT the car (which is 2 out of 3 times) then switching will DEFINITELY be the car.

There's a 1 in 3 chance that the current door is the car. You know one of the doors isn't the car. And you also know that you won't switch to that door. So if the current door is not the car (which is a 2 in 3 chance) then the other door is definitely the car.

I hope some of the things I have said is helpful

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But I thought we knew we were on a goat... Is the damn door open or closed? lol Are we saying the last third is the option to stay where we are?

No we don't know if we're on a goat or a car. One other door is opened and revealed to be a goat. We are asked if we want to switch to the third and final door or stay on the first door.