anything Posted November 11, 2009 Report Posted November 11, 2009 You have a fair coin, and when tossing it you are looking for patterns, either HTH or HTT, you count the number of tosses it takes until you see each pattern. You do this many times and get an average number of tosses for each pattern. Which of the following is true? a) The average number of tosses until HTH is larger than the average number of tosses for HTT b) The average number of tosses until HTH is the same as the average number of tosses for HTT c) The average number of tosses until HTH is smaller than the average number of tosses for HTT Quote
beth1974uk Posted November 12, 2009 Report Posted November 12, 2009 You have a fair coin, and when tossing it you are looking for patterns, either HTH or HTT, you count the number of tosses it takes until you see each pattern. You do this many times and get an average number of tosses for each pattern. Which of the following is true? a) The average number of tosses until HTH is larger than the average number of tosses for HTT b) The average number of tosses until HTH is the same as the average number of tosses for HTT c) The average number of tosses until HTH is smaller than the average number of tosses for HTT your not doing a maths degree are you??? takes me right back!! Quote
Anne1599968726 Posted November 12, 2009 Report Posted November 12, 2009 Too much time on your hands? Unhealthy fetish for statistics? Desparate cry for help? Or all of the above? Quote
DavidOps Posted November 12, 2009 Report Posted November 12, 2009 I'd say B, It's a fair coin the result is either H or T totally at random (given a random fair toss [Not sure i really give a toss]) So there is no way that A or C can apply. If they do then you have not conducted enough coin tosses to get a true average reading. It's like tossing it three times and getting HTH then saying "on average this coin always comes up Heads" statistically true but massively flawed. Quote
high.as.a.kite Posted November 12, 2009 Report Posted November 12, 2009 (edited) The answer is B. You're going to get a result the first time you get a HT turn up in the sequence, the next toss determining the result. The average number of tosses before HT comes up will be the same for either result. And since the coin is fair then the H or T on the third coin in the sequence will be 50/50. If the target patterns differed by more than just the final toss then you could get a difference. i.e. The target patterns were HTH & TTH. Edited November 12, 2009 by high.as.a.kite Quote
eeyore Posted November 12, 2009 Report Posted November 12, 2009 Too much time on your hands? Unhealthy fetish for statistics? Desparate cry for help? Or all of the above? A cry for help Quote
high.as.a.kite Posted November 12, 2009 Report Posted November 12, 2009 I think the t-shirt reads: Statisticians do it whilst tossing! Quote
jablonski1599968753 Posted November 12, 2009 Report Posted November 12, 2009 Hu!!! Got any stats on buttered toast... Quote
crazyman Posted November 12, 2009 Report Posted November 12, 2009 Hu!!! Got any stats on buttered toast... 100% chance buttered side down. Quote
high.as.a.kite Posted November 12, 2009 Report Posted November 12, 2009 100% chance buttered side down. Buttered toast + cat + duck tape = perpetual motion machine! Quote
anything Posted November 12, 2009 Author Report Posted November 12, 2009 I'm a 4th year statistics student No one has posted the correct answer yet. Just wanting to see if anyone can get it right with a plausible explanation Quote
DIEM Posted November 12, 2009 Report Posted November 12, 2009 ^^^^a scouse "bamber gascoigne"^^^^ Quote
Steve1599968621 Posted November 12, 2009 Report Posted November 12, 2009 All of them or none of them. Quote
braddels Posted November 12, 2009 Report Posted November 12, 2009 Got any stats on buttered toast... the mythbusters did an experiment on it. here are the notes from the show Buttered Toast: which side does it fall on? There were two things being tested here: 1. If buttered toast falls off the table, does it prefer to land butter side down 2. If a buttered toast falls through the air, which side does it prefer to fall on? First (Adam's) rig: Adam's rig most closely replicated a piece of toast falling off of a table top. Testing with a control sample of unbuttered test, the dominant behavior was for the toast to flip once and land top side down. They didn't need to do any more testing with actual buttered toast, as the rig clearly had a bias. Second (Jamie's) rig: Jamie's rig tested whether or not, all things being equal, which side toast prefers to fall on. It shoots toast straight down. With control sample testing, toast kept landing down. Once again they were statistically challenged, as they stopped after 10 samples. They determined that 3 ups and 7 downs was enough to show a clear down bias, and once again, if just one of those had been different, they it would have been 4 ups and 6 downs, which doesn't seem biased at all. Third rig: based on Jamie's original design, but with way more over-engineering to be more automated, regular, and MythBuster-y. A conveyor belt toaster dropped the toast off onto a second conveyor belt that carried toast over to Adam, who marked the toast and loaded it into a dropper that was then released with a switch. * 11 up and 13 down with control sample * 12 up and 12 down with buttered sample They determined this to be "less biased", so they then brought it to the roof of MythBusters HQ. From the top of the roof: * 26 up and 22 down with control sample * 29 up and 19 down with buttered sample Jamie's theory was that for a lot of the buttered toast that landed butter side up, the buttered side was pressed in, forming a cup that affected the way the toast dropped. Quote
spiky_dave Posted November 12, 2009 Report Posted November 12, 2009 The answer is B. You're going to get a result the first time you get a HT turn up in the sequence, the next toss determining the result. The average number of tosses before HT comes up will be the same for either result. And since the coin is fair then the H or T on the third coin in the sequence will be 50/50. I agree entirely... Ok anything, explain how a 'fair' coin can be more likely to generate one sequence than another (the sequences being the same length)? Quote
anything Posted November 12, 2009 Author Report Posted November 12, 2009 The answer is a, i will give an explanation when i get back from work On average it takes 8 tosses before you see HTT, but it takes on average 10 tosses before you see HTH Quote
Tjah1087 Posted November 12, 2009 Report Posted November 12, 2009 I think the confusion is arising from the fact he is looking for the average number of tosses until they occur, rather than the probability they will occur. Please post your proof. Quote
-flyzone- Posted November 12, 2009 Report Posted November 12, 2009 its simple realy because the coin is "fair" avrage for htt will eb the same to hth out of 100 tosses.. that would only work computer simulated though.. you can actuly controll the outcome of a coin toss by how u flick it so the answer could be a, b and c.. Quote
Tjah1087 Posted November 12, 2009 Report Posted November 12, 2009 There is a similar problem where TTH is more likely to occur before HTH. I think you may be confused. Quote
The Geoff Posted November 12, 2009 Report Posted November 12, 2009 Yeah, this is a trick question with something non-intuitive going on I reckon.... Basically, you keep tossing coins until you get a HT, then the next toss is what decides it...which is 50/50. You'll probably get a bunch of TTH and THT in the process... But....if the first coin is a H, you're then looking at cutting out the first of the HT... Intuitively I'd say it's 50/50, but given the odds of Anything being a cleverdick (tending to one ) I'm going with HTH being more likely, (a). Quote
-flyzone- Posted November 12, 2009 Report Posted November 12, 2009 ah i agree with geoff now.. since it is a fair coin your it's more likely to go hth then htt... since hth is fair over htt isnt:rolleyes: Quote
-flyzone- Posted November 12, 2009 Report Posted November 12, 2009 ah i agree with geoff now.. since it is a fair coin your it's more likely to go hth then htt... since hth is fair over htt isnt:rolleyes: Quote
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