Anyone good at calculating probabilities?

I ride a motorcycle and have in the last 4 years run out of petrol 6 times on the road. The characteristic of running out are: driving along then the bike stutters as the first cylinder drops out then, quickly after each of the other cylinders drops out with power being lost all the while. From first stutter to engine dead is about 1/4 mile + whatever you get from free-wheeling to a stop - say 1/3 from first warning to stopped.Most of my mileage in to work and back: 18 miles each way - same route more or less, out and back. The bike is my only form of transport though so is used for all other journeys of which there are plenty during the week. On the route into work, there are 6 petrol stations (where there is a petrol station on opposite sides of the road within a hundred yards or so I count them as 1 station).The reason for running out are threefold. The petrol tank is small so you tend to want to run it as empty as you can before filling. The petrol gauge isn't all that accurate. The tank is about a 1/4 empty before the needle drops off 'full' and is about a 1/4 full when the needle reaches 'empty'. There is no reserve facility which can be switched on. Sometimes I am aware of that I am in the danger section of the 'empty' zone and intend to fill up - but forgetEach time I have run out it has been during a work trip. What is the probability that:a) on each of the six occasions I ran out, I managed to stutter to a petrol station.b) what is the additional decreased probability that on on 5 of the 6 occasions, the petrol station I stutter into the same petrol station.Note: I have no preference for filling stations except the one closest to home (which I have not rolled into on empty). All the other stations are used from time to time without particular favor. When I'm low I'm low and not particularily fussy. When I'm out I not fussy at all!ThanksIanThis message has been edited by iano, 05-Sep-2005 05:00 PM

I'm pretty good at simple probability math (I'm too rusty to be good at the harder stuff).But you really haven't supplied enough information to get anything more than a rough estimate that might be completely wrong.Some questiosn to consider:1) How many miles do you get from a full tank ?2) What proportion of the time do you run out rather than remembering to refill ?3) What proportion of your milage is on non-work trips and how variable is it ?4) Where was your last refill before running out ? Was it the same place each time ?5) How are the petrol stations distributed ? Is it even or not ? Is the one you have rolled into on empty close to any of the others ?6) Have you been going the same way each time you ran out ?

that the situation you describe will continue.Have you ever thought about filling up before it gets empty? If you refill when it's only half empty you will still use the same amount of gas, spend the same overall amount, but never run out of gas.

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Aslan is not a Tame Lion

You bring back memories. But it is a long time since I rode a motorbike. There was no petrol gauge, but there was a "reserve tank". My habit was to run it dry, then switch to the reserve while looking for somewhere to fill up.But can't you use the odometer to somewhat estimate when you will run out. You probably have a reasonable estimate of how many km you can do on a full tank, so just fill up 50 km before that.

Hi PK1)I don't think the mileage from the tank is part of it as it's more to do with probabilites of things happening "when I run out" than probabilities of "running out at all". But I'd get about 170 miles from full to low-low.2) I spend a quarter of my time at empty so its always a matter of being aware at which point in 'low' I am. I'd never arrive at low unaware but will typically be aware a fill is coming up (say on the way into work) but then forget on the way home, or am aware at the start of the 'last drop journey' but then forget. The proportion of running out vs refilling in time is negligable. In 4 years I'd have filled up over 300 times of which 6 were run-outs3) about 70% of mileage is work - not variable in itself but I might divert to visit someone or go to bible study after work or go to music practice or shopping or whatever4) Because of the variety of my riding I fill up all over the place although because work is the majority, those work route garages would get the lionshare of my business. But if I'm in low low and leaving home I would tend to fill up at the garage around the corner. If I was just low, I'd fill up along the way. There is no order to it really. If I was just hitting 'empty' and pulled in for a paper for example, I wouldn't necessarily fill up.5) petrol stations from home: 0 miles, 1 mile, 5 miles 8 miles 12 miles, 15 miles. work is 18 miles away. It would be the opposite on the way back. The one I rolled into 5 times is the one 1 mile from home, 4 times on the homeward journey, once on the outward journey. The 6th occasion was not a station on this route. I remembered I was low, took a turn off toward a petrol station I knew and started stuttering in sight of it. That was a homeward journey tooNote: on all occasions, the rolling into the station occurred on the last stutters not in the intitial stages. Either I came in on a half a cylinder or was free-wheeling.

Your probably right Ah but then I'd have to stop to refill twice as often. Somewhere I've said that I'm impatient. Once I get going I'd be bursting for a piss and not stop til I got where I'm going. Plus all the car drivers whose mirrors I've clipped in the nutbag traffic I have to negotiate each day might catch up with me.Method in the madness

Yeah the old reserve tap. Excellent idea but it got evolved out. Scrabbling for it whilst overtaking a line of traffic with a truck coming the opposite way. They were the days I would but it's broke. I keep on getting a new drive for it but it's brittle and everytime I get a front tyre changed the clowns break it when refitting the front wheel. You don't need a speedometer in Ireland! The bikes got 65,000 miles up but shows only 24,000 on the clock. I'm a Christian though so wouldn't mislead anyone when the time comes to sell I can estimate pretty good as I keep an eye on when I hit empty. It's forgetting that causes the problem. 6 outs from 300 or so ain't bad. I could probably carry a 1/4 litre under the seat too. So far though things have worked out

Just a little disagreement on the implication there. In my experience there are many Christians who would mislead, and many non-Christians who would not mislead.To stay on topic (of probabilities), my tentative assessment is that being a christian, and not wanting to mislead, are stochastically independent random variables.

1) The milage is important. For a start it tells us that your quarter-tank is further than the round-trip to work and back. (170/4 = 42.5 versus 18 * 2 = 36).2) You only forgot to refill in time 2% of the time.3) On the basis of this, the non-work mi lage probably isn't significant. Partly because it is less than 1.3 of the total milage - but also because the trips are usually shorter.4) That isn't the question I was asking. On the 6 occasions you ran out was your previous refill at the same gar age or not. It probably isn't important now.5) 4 out of 5 times on the homeward trip is probably significant. It means that you're only a mile off from the station you prefer to use. The fact that the there is a petrol station very close to your home is also significant.In my estimation, answers 1 & 5 are probably significant. You forget to fill up at your preferred station on occasions when you still have most of that quarter tank. If you had a little more you could delay refilling until the next outward trip, at the station you prefer to use. So it only takes a relatively small misjudgement to get to the situation where you have to refill at that station. There may be some warning sign (perhaps noticed subconsciously) which hits with about 4 miles worth of petrol..lThis message has been edited by PaulK, 09-05-2005 02:19 PM

I agree that non-Christians do good and Christians do bad. This particular Christian however, up to 4 years ago, would given the bike good polish, replaced the worn footrest rubbers (the only obvious tell tale sign of its age) and keep a dead straight face as he said: "...and a gentle 24,000 miles its been too"So, what chances 6 petrol outs resulting in relief and 5 of those stations being the same one. Stick that in your stochasticial pipe. When I see white smoke I'll know the pipe has produced a pope

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Romans 10:9-10: " if you confess with your mouth the Lord Jesus, and believe in your heart that God raised Him from the dead, you will be saved....."

I would take this as fairly good evidence that the mileage you get on one tankful is fairly close to an exact multiple of your round trip mileage.But perhaps it is not even that. Perhaps your forgetting to fillup is infrequent, and at other times you normally fillup at your favorite station. In that case, you are just seeing evidence of consistent mileage, as PaulK seems to be suggesting in Message 9 LOL

I'm not arguing with you, if there are relevant issues then I'd like to see them in there. I have no idea of the probability so am curious about it. I don't see the significance of a 1/4 tank being enough for a round trip influencing the chances of coasting into a petrol station. Because of the wildly varying driving my 1/4 tank can appear anywhere, anytime on any journey. 1/4 tanks doesn't make me go looking for a station. It's low-low (or biting into 1/8th that gets me mildly interested) Fair enough Just calculating: 36 mile round trip x 250 work days = 9000 miles/year. With no speedo I don't know but would say another 4-5000 given where friends/parents live, bike is sole transport etc. It would be mostly shorter and frequent than long journeys I suppose but I live well outside town so 10-20 mile trips aren't unusual I couldn't say as I don't keep track. I know by and large I fill at the next garage I see when I figure I'm in the low-low zone. Given the random location of a low-low I would guess I didn't fill at the same garage. In the case where the garage wasn't the same one I rolled into on the other occasions, I didn't fill there before - it is off track and I went seeking it. Given the amount of garages around running out isn't that likely if I pay attention at low-low. Also, if I was on a journey in unknown territory, I wouldn't let it run so low. I manage the risk because there are garages around. It's the forgetting that is the issue it seems. If you reckon a physcological preparedness for more risk is a factor the following should disuade you from it My 'preferred' garage is about 150 yards away. If I don't want petrol but needed smokes or milk I have been know to drive there!(like, thats 300 yards round trip if I gotta walk - ugh!) If I ran out a mile from home I'd ring a taxi!! (Sheesh this is revealing a little more that I planned ).I've had every bike I've ever owned stolen from me. I have two gigantic ground anchors: 1 at my house and one at work. Otherwise I wouldn't tend to leave the bike out of my sight except where theres plenty of people around. Leaving at the side of the motorway (prior to my home stations) for two yobs in a van to pick it up would be a real no-no. Pushing a dead 600 more than a 100 yards is not for the faint hearted either.Also I wear all the trappings of an Irish biker and it ain't no fun tramping around in that gear.Nope, running out wouldn't be fun. Which reminds me. I knew I had 7 run outs when I posted but could only remember 6 so described them. Talk of leaving the bike unattended has made me remember the 7th. I did the precise same thing and entered the same garage of the other 5. But it was late and the garage was closed. I pushed it around the back and locked it. Taxi up the next day. (I knew I was a lazy so-and-so). It was a homeward bound journey but from the pub not from work. Sound enough thinking. However I wouldn't fill on 1/4 tank there. I typically but not always fill on 1/8 or less. If I forget my favorite garage I should run out near work not near homeI've had some bikes that give 'better' warning alright (and most will get you alot further than a third of a mile after a warning). You would get little power loss indicators under acceleration etc. My Fazer is a bummer in that regard (in addition to glass-like speedo drive). I'm not making it up honest. One second fine then a little hesitation then your into chugging mode and wiggling from side to side to get the dregs into to fuel pump.thanks for thinking about it though...

Don't think this hasn't had me thinking but there are too many variables. First my favorite garage ain't that favorite. If on 1/8th tank I'd be perfectly safe to pick one of 3 garages on the run to work but would pick this one as it is at the start of the journey. It only gets preference in that limited situationA match between tank range and route doesn't fit given the multitude of variable during a 170 mile tank range. That's 4.7 roundtips to work. I do get out a bit you know...

One more time at the same place supports the view that there's a casual factor biasing things in favour of you winding up at that particular station.As you have seen the relationship between the quarter tank and the round-trip distance is a possible factor. A quarter tank is a bit more than you need for the round trip, so if you have close to a quarter tank when you set out you probably won't need to refill. And if you start off with the idea that you have enough, then you're that bit less likely to stop. Thatt comes down to thinking you can make 36 miles when you can only manage 34 2/3 - 35.

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If on 1/8th tank I'd be perfectly safe to pick one of 3 garages on the run to work but would pick this one as it is at the start of the journey. It only gets preference in that limited situation

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On the figures you've given, the problem is that you DON'T always do that on the way back (with 1/8 tank you should make it all the way). That's 6 out of 7 cases.And on the one occasion you had to stop on the way out you really did forget that you were nearly out.s