# A little maths riddle...

Discussion in 'Off Topic [BG]' started by Hellsgamerz, Jul 28, 2004.

1. ### Hellsgamerz

My dad was reading a book the other day with a riddle in it. It didn't make any sense to me at first, but I got it in the end. Made me wonder wether I'm stupid or just bad at math. Here it is:

On a game show, you get to pick one out of three doors. Behind two of them is a goat, behind the other is a car. After you pick one of the doors, the game host opens one of the doors with a goat behind it that isn't the door you picked. You are then left to choose wether to stick with your choice or pick the other door.

Now, the question is: what is the best to do? Chance, stick with you choice, or doesn't it matter at all?

Solution: (select the text to see it)

The best thing to do is change. You then have 2 out of 3 chances to get a car

edit: spelling errors, correction thanks to BlackBird

2. ### Bob ClaytonModeratorStaff MemberSupporting Member

Aug 14, 2001
Philly Suburbs
not that i disagree with you. but how do you figure? like, mathmatically speaking.

3. ### Mon RomineeBanned

Appears you would have the same chances either way. If the car appeared in the other door, opposite of your choice, you still wouldn't get it...

4. ### Hellsgamerz

Spoiler again:

When you first get to pick, 2 out of 3 chances are that you get a goat. So when the host tells you to either stick or change, you're best to chance. That way, if you had a goat you would now have a car, and the odds are on you getting a goat.

5. ### Jack

Sep 6, 2003
Newcastle, UK
I disagree.

Chance of car first choice = 33%

Chance of car after host opens door = 50/50

No matter which door you pick, your odds are still 50%.

Unless of course he opens the door you picked and reveals it to be a goat, in which case Id change.

6. ### temp5897Guest

Ok this is very easy and I heard this years ago. I figured it out within ten seconds of hearing it, because it is so simple.

The answer is that you have a 2/3 chance of getting it if you switch. The reason why is because you have a 1/3 chance of picking the right one initially. That means there is a 2/3 chance that the right one is still left behind the doors. One of the doors is eliminated for you. *There is still a 2/3 chance that the correct answer is behind one of those doors* Since one of them is eliminated for you, you have a much better chance of winning by switching to the door that is left that you didn't pick. If you don't think it's true, run the experiment with a marble and three overturned cups about 100 times and see what your correctness ratio turns out to be. Nothing like a little emperical evidence to support facts.

A 50% chance of getting it right is just wrong.

7. ### fastplant

Sep 26, 2002
Connecticut
I understand why, but I still don't buy it.

8. ### Lloyd Christmas

Door 1 = Goat
Door 2 = Goat
Door 3 = Car

You pick door 1, host would then open door 2 and show you the second goat. You now choose between door 1 and 3, if you switch you get the car.

You pick door 2, host would then open door 1 and show you the second goat. If you switch from door 2 to door 3, you get the car.

If you pick door 3 the host would open either door 1 or 2, if you switch you will get a goat. If you are a hillbilly, this is a good thing.

2/3 times you get the car by switching.

9. ### Hellsgamerz

You guys got it faster then me . Anyway, if you still don't believe me, I've got a spreadsheet to simulate this.

10. ### fastplant

Sep 26, 2002
Connecticut

I want to see it, I still don't buy it. I understand the math, but I don't think switching will prove this in a real situation.

11. ### Zon Bass

Jan 20, 2002
Dallas, TX
But I like goats

12. ### Hollow ManSupporting Member

Apr 28, 2003
Springfield, VA
Jared is right... I've heard this problem, and I solved it out in high school. It doesn't seem like it makes sense when you hear it and think it over, but if you work through all the possible combinations, you really do have a better chance if you switch doors.

13. ### GrooveWarrior

I have another math riddle:

Three guys go on a road trip to catch a Christian McBride Band show (hey, it's my riddle, I can make it whoever I want). They have to travel pretty far (because he never comes to the midwest) so they decide to split the cost of a hotel room.

The room is \$30 so each guy chips in \$10. They go to the room and get settled in. Then the manager realized he forgot to tell the guys that the room was on special tonight for \$25. The manager gives the bellboy (I know a hotel that has \$25 room wouldn't have a bellboy, work with me here) 5 \$1 bills to take up to the room and give back to the guys.

On the way to the room, the bellboy realizes that the guys will never know how much of a refund they were supposed to get, so he pockets \$2, figuring he will just give \$1 back to each guy. When he gets to the room he gives each guy a dollar back, and they are happy.

Since each guy got a dollar back, that means they spent \$9 each on the room. \$9 times 3 is \$27, and the bellboy pocketed \$2. \$27 that the guys spent on the room plus the \$2 the bellboy pocketed equals \$29.

WHAT HAPPENED TO THE OTHER DOLLAR FROM THE ORIGINAL \$30?

14. ### paniak17

Mar 19, 2004
Northwest, Indiana
It's a wrong formula. It should be: 3 x 9 = 27 - 2= 25 + 5 = 30. All of its there.

15. ### GrooveWarrior

I know the solution. You didn't have to ruin all the head scratching for everyone else.

16. ### paniak17

Mar 19, 2004
Northwest, Indiana
o sry! ill make it white or sumptin holdon

17. ### temp5897Guest

The guy's didn't end up paying 9 dollars a piece for the room though. They paid 25/3. It's an incorrect assumption on the wording of the problem, is it not? It just so happens that they were ripped off by the bell boy for 2 of their 5 dollar refund.

The correct formula should in the end be 25/3 + (3+2) = 30, or that the two dollars is subtracted from the 27 dollars, not three dollars subtracted from 30. Right? I don't know if I explained that well...I honestly don't know if this is the answer but it seems to me like the way the question is posed is just incorrect (in terms of its supposed "answer"), and that's where the solution lies.

18. ### paniak17

Mar 19, 2004
Northwest, Indiana
that was the whole point of the riddle, to make you think one way that seems right, but isn't, and then your job is to redo the problem into its correct wording so that it makes sense.

19. ### BlackbirdModeratorSupporting Member

Mar 18, 2000
California
I'm glad you got it in the end, but you're wrong, with the bum option eliminated, you have 1 out of 2 chances to win. Option 3 is out, remember?

Maybe you should give some more attention to your English.

20. ### Jazzin'...Bluesin' and Funkin'

yah, chances are that u picked a goat in the first part. so then if u did pick a goat, then the dude will now show u the other goat. now the best thing to do is switch.