A fellow finds himself at a party at Bill Gates' house, standing next to the great man himself, and Gates says to him, "Hey, how many people do you think are here?" The fellow looks around and says, "Jeez, I don't know. Eleven hundred?" Gates says, "That's right! You know, you're very good with numbers. Are you into games of chance, by any chance?" "Oh, no," the fellow says. "The chanciest thing I get involved in is tossing a coin." Gates says, "Well, do you think you could toss a coin 10 times in a row and call it correctly every time?" The guy says, "I don't think so." Gates says, "Well, do you want to make a bet? Because I can do it. After all, I'm Bill Gates and you're not." The fellow declines. "No, I don't want to make a bet. I don't think I can call it 10 times in a row. I don't think you can either. But I need the cab fare to get home, so I don't want to bet." Gates says, "Do you think there's anyone in this room who could call it correctly 10 times?" The fellow says, "I suppose there's a chance, but it's a pretty small chance." Gates says, "I'll tell you what. I'll bet there is someone who can call it correctly. And here's what calling it correctly consists of: If I toss the coin, I can call it, and if I'm right, that's a win for me. Or, if I toss the coin and you call it incorrectly, that's also a win for me. Got it?" "So," Gates says, "tell you what. I'll make you a bet. I'll bet you my $10 million to your $10,000 that it can happen in this room, that there's one person who can win 10 in a row." The guy says, "You're on." Was he right to take the bet? Why or why not?
I dont think it has anything to do with math. Is the other guy even allowed to call it when Gates tosses the coin. Bill Gates says that he himself can call it when he tosses it. Well is the other guy even allowed to "call" it?
well 1/2^10=1/1024 so since there are 1100 people there the odds of someone calling it right would have to be pretty high (i would think since the chance of any individual losing is 1023/1024, the chance of all 1100 losing is (1023/1024)^1100 which should be a pretty small number). so no i definitely don't do it. i especially don't do it if my roommate from last year is there. a math teacher in high school essentially did this same. he had written true or false 10 times on a paper and then had the class just write true or false 10 times to see who would get the most right. somehow, my friend went 10 for 10.
If the guy is struggling to keep cab fare, why does he have $10,000 to spare? My guess is that he doesn't pay up if he loses, so there's no risk. Therefore, it was a great bet for him to make. As for the correct answer, there's a 2^10 probability that he will get all 10 right. (the Bill calling it correctly or OtherGuy calling it incorrectly is irrelevent, since only one will be calling it). That is 1 in 1024. With 1100 people in the room, there's a good chance someone will get it right. However, I'm not sure exactly what that chance is, and don't feel like trying to figure it out. But if the chance turns out to be more than 99.9%, then taking the 1000:1 odds is a bad idea. If it's less than 99.9%, then the odds are with the PoorGuy, although he's still most likely going to lose his $10k. (in this scenario, if he repeated the entire experiment 10000 times, he'd likely come out ahead) Is this the right answer? maybe, maybe no. EDIT: f4p figured out the correct number. Obviously, the chance is a bit better than I thought, so the odds favor PoorGuy, except that he probably can't afford to lose $10k, seeing as how he wasn't willing to risk his cab-fare earlier. EDIT #2: RM95, stop using my computer and logging in under your name, dammit. This is Major.
ok well my calculator says that (1023/1024)^1100=.341385 That means there is essentially a 1 in 3 chance that everyone loses and you collect. So now, I say I would take the bet. What's 10k when you have a 1 in 3 shot at 10 million. this of course is all contingent upon the fact that i have understood the problem correctly. if i haven't, then i say you just kick bill's ass and take the 10 million and run.
Anybody ever listen to Click & Clack, the 2 MIT auto mechanics that host "Car Talk"? Man, I loved their show... Yeah, I know... "what does that have to do with this riddle?". Everything : http://cartalk.cars.com/Radio/Puzzler/Transcripts/200046/answer.html
Having RM95 logged into your machine, Major, you can really teach him never to do it again: post a "Who Thinks The Rockets Uniforms Suck?" in the Rockets forum under his name, and blammo - one contest lost in the finals, one lesson learned.
You'd think he'd realize that he wasn't logged into his since he has the white screen and I have the blue one.
Having RM95 logged into your machine, Major, you can really teach him never to do it again: post a "Who Thinks The Rockets Uniforms Suck?" in the Rockets forum under his name, and blammo - one contest lost in the finals, one lesson learned. During our picture-posting contest for our showdown, I posted "A reasons to vote for me" post with classy (but hot) pictures. I almost went over to his place and posted "reasons to vote for me" under his name with some not-so-attractive pictures. But in the end, I decided I'm too nice to do that.
That answer is not right: RAY: And let's take that 1,024 people and make 512 pairs of people. TOM:: Yeah. OK. RAY: OK? And each one of those pairs will do a coin toss. Well, obviously, one is going to . . . one of them is going to win. This isn't true. What if you toss the coin and I call it correctly. Under the rules, that isn't a win for me. Or, if I toss the coin and call it incorrectly, that isn't a win for you. So neither one of us won in that scenario. That destroys their whole "one person must win" concept. For reference, here are the rules: And here's what calling it correctly consists of: If I toss the coin, I can call it, and if I'm right, that's a win for me. Or, if I toss the coin and you call it incorrectly, that's also a win for me. Got it?
