"If the prize is behind No.2, the host shows you No.3. So when you switch, you win if the prize is behind No.2 or No.3. You win either way! But if you don't switch, you win only if the prize is behind door No.1." If the host shows you No. 3, how can you win if the prize is behind No. 3? He has already shown it to you, thus it is empty. Pugs
Ah, I get it. Yall are right. Interesting little hypothetical. Only works in the scenario listed (Monty revealing the empty door). If it was a random door selected, and you the contestant was forced to switch automatically, then he'd be 50/50.
Please elaborate Sam, I'm pulling my hair out....how does Monty revealing the door bump you from a 50% chance to a 66% chance? Pugs
Actually, the answer's 2/3. As a hint to the reason why, the answer to the related question, "I have 2 siblings. The older one is female. What is the probability that the younger one is male?", on the other hand is 1/2. I can't afford to take the time from work to actually use my brain any more today , so a longer explanation, if needed, will have to wait.
Because he only reveals an empty door, not a random door. If you consider doors (B + C) a subset, then in effect taking the option to switch after the reveal means that you have the option of choosing the (B + C) subset of doors in total. That subset has a 2/3 chance of having the prize. Obviously, one of those 2 doors in the (B+C) subset is empty, and the host reveals that door, but the subset's chances of winning remain 2/3. If the host had no idea what was behind the doors, and just happened to randomly open door C and it was empty, then you'd be back at 50/50.
Here is a riddle for you: Question: Why did Michael Jackson die? Answer: He got food poisoning from a 10-year old weiner. HARRRRR
So why is it 2/3? Is it because the initial probability runs M:M - 1/4 F:M or M:F - 1/2 F:F - 1/4 but by her being female it eliminates the first choice and of the remaining choices it is 2/3 chances of being 1 female and 1 male?
Yep. Stolen from http://www.straightdope.com/classics/a3_189.html, where Cecil Adams screws up the Monty Hall problem. From the final paragraph:
Again with the damn Monty Hall question. This was discussed to death a couple of years ago already. If search worked, I'd link it.
Sam, I think whether the host knows what's behind the door is irrelevant. Had the host opened the door to the car, the contestant will no longer have the option to "choose" because the game is basically over. In that case, the question only applies with the host always opening an empty door, making the host knowing where the car is meaningless. I agree with the answer of "always switching to door C".
Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I am not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool, you would have counted on it, so I can clearly not choose the wine in front of me. You only think I guessed wrong - that's what's so funny. I switched glasses when your back was turned. Ha-ha, you fool. You fell victim to one of the classic blunders, the most famous of which is "Never get involved in a land war in Asia", but only slightly less well known is this: "Never go in against a Sicilian, when *death* is on the line.". Hahahahahah.
I was asked this a while back and it took me about 2 hours to get it. It's become one of my favorite logic problems of all time. Anyhow, I don't like to give away answers but the bingo number is 47. Here's one: rich guy needs to carry a lot of his gold so he hires 12 men who carry 12 bars that weigh 12 kilos each. One capable guy decides to shave 1 kilo from each bar in such a manner that it is impossible to detect visually or by feel etc... At the end of the trip, the rich guy is tipped off that he has a thief amongst him. There is a large scale he can use (like the kind you can step on and it displays a digital output) but the scale can only be used once due to whatever -input reason here-. What's the rich guy's strategy using the scale only once to find the thief.
HAHA, this reminds me of the Princess Bride where the smart man starts using circular logic and ends up drinking to poison. Smart Guy: How did you know I would choose this cup? Hero: I didn't. I poisoned both cups. I developed immunity to the poison while I was traveling in another country. Smart Guy: Damn you.... *bleh*
Hmm, seems easy. Let me give it a go. Have 1st guy put one bar. 2nd guy put 2 bars. 3rd guy put 3 bars. Etc. THEN weigh The toal weight should be 78. 78 - weight on scale = person # who was the thief.
Four guys are buried up to their heads in the sand, 3 on one side of a wall and one on the other side. They are shown four hats, 2 black and 2 white. Each man then has a hat placed on his head. The guy who is alone on one side of the wall cannot see the other guys. The other 3 are in a line, and each guy can only see the ones in front of him. They are told that they collectively have one guess. One of the men must say what color hat he is wearing. If he is right, they all live, if he is wrong they all are killed. They are arranged like this: W B W | B If they are numbered 1 to 4 starting on the left, with the vertical line representing the wall and the W and B corresponding to the white and black hat respectively, which man knows the answer and why?
The second guy probably knows the answer. If guy #1 saw B B or W W, he'd know that his hat is the other color. Thus the combination must be B W or W B. The second guy sees W and knows he must have B since that is why the first guy didn't answer.
Here's a good one that is amazingly simple yet difficult to figure out. One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. The distance between LA and NY is about 5000 miles. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?
