# what is the (conditional) probability of exploding when filling your car up with gas?

What is the probability that you will cause an explosion when filling up gas?

I like to wait inside my car when my car is filling up with gas. I do this to reset my trip odometer, stay warm, etc. One — and only one — of the local gas stations has a sign (pictured below) warning me to not get in and out of my car when fueling up. The implicit claim here is that getting in and out of my car raises my conditional probability of exploding. I as curious to see if (a) that claim was true and (b) how significant that rare risk would be if it were true, and (c) why only one gas station wants to protect me from this risk.

Snopes has some interesting data about this issue based on a PEI report [Link] The data is apparently a mess, but it looks like there were 81 fires over ~7 years, and information about 64 of these fires was available for further analysis. Most of the fires occurred in the most recent year. I assumed that maybe older fires were less likely to be recorded and therefore assumed that this represented 2 years worth of fires (~24B re-fuelings). The report implicates women in entering the car but the report’s authors don’t actually identify gender in their statistics (read the Snope article). I’ll take this into account.

It’s worth noting that men get struck by lightning way more than women. Maybe women balance this out by causing more fuel fires?

Claim (a) appears to be true. Let’s say there are 81 gas explosions in 2 years (24B refuelings). That is a base rate of 3.4×10^-9, a rare risk. This doesn’t give any insight into whether going back into one’s car is a bad idea, so let’s look at that issue further. To do so, I will assume that the 17 fires are randomly either caused by reentering or not reentering one’s car. Then, we know:

P(fire and reenter) = 1.5×10^-9

P(fire and no reenter) = 1.0×10^-9

Of course, we want to find P(fire | reenter) and P(fire | enter). To do so, let’s assume that women do 36% of all fuelings (same as the proportion of miles driven by women) and that women reenter their cars 50% of the time and men reenter 10% of the time.

P(fire | reenter) = 6.25×10^-9

P(fire | no reenter) = 1.4×10^-9

Fires in cars where someone reenters their car occur 4.5 as often as when they don’t. If we look at an extreme example where all women reenter but no men do

P(fire | reenter) = 4.22×10^-9

P(fire | no reenter) = 1.65×10^-9

Here, people that reenter (all women) cause fires 2.5 more than those that do not reenter (all men).

But those that reenter may not always cause fires at a higher rate than those that do not reenter – it all depends on how often people reenter their car. Let X = the probability that people reenter their cars while fueling:

P(fire and reenter) / X >= P(fire and no reenter) / (1-X)

This is true when X < 0.591. This appears to be true, but it's a fairly realistic number even though I bet it's a bit high. Given the rarity of fires, people that reenter probably do not cause fires at statistically significantly higher rates than those that do not reenter.

Any risk that happens about once every billion fuelings is very rare. I will not fuel my car that often over the course of my lifetime, so I can expect to escape without causing a fire.

Let’s compare the risk associated with causing an explosion due to reentering one’s car to the risk associated with dying in a car accident. To do so, let’s assume that one drives 300 miles between refuelings for an apples to apples comparison. Then, the risk of dying between refuelings is 3.3×10-6 (1.1 deaths per 100M miles driven). When compared to the risk of exploding given that you reenter, you are 528 more likely to die driving than explode when reentering your car while fueling.  Therefore, I’ll conclude that if a risk from reentering my car exists but that it’s fairly insignificant (Claim b), which explains why most gas stations are not concerned about warning me (Claim c).

Have you ever caused a fire while filling your car up with gas? Do you even know of anyone second- or third-hand who exploded while fueling?

#### 13 responses to “what is the (conditional) probability of exploding when filling your car up with gas?”

• David

Interesting. I remember 10-15 years ago, there were several relatively-highly-publicized incidents of people who caused major explosions via a spark from re-entering their car. It was following those incidents that I started seeing the “Do not get back in your car” warnings at gas pumps.

More recently, I’ve noticed warnings about cell phones, like the one in your picture. I suppose I could imagine a scenario where cell phone usage is distracting and you do something stupid while texting your friends (freak gasoline fight accident?), but the local gas station I use instructs me that I must turn off my cell phone while fueling. This doesn’t make any sense to me — how is my powered-on, but in my pocket, cell phone going to cause a gasoline fire?

• Sanjay

I’d expect few responses to “Have you ever caused a fire while filling your car up with gas?”. Surely fire-causing readers are likely dead. Or zombies.

• matforddavid

This is one warning that has not yet crossed the Atlantic. UK forecourts are self-service (generally) and there are no restrictions about getting in and out of the vehicle, so passengers can go and pay to speed up departure. We do have warnings about cell (mobile) phones.

I like the ambiguity of the text in your sign:
If a fire occurs:
Do not remove nozzle and leave the immediate area.
Does that mean Do not remove nozzle and do not leave the immediate area?

• prubin73

One of the main reasons to reenter the car is to stay warm, and people trying to stay warm may be inclined to run their engines (to keep the heater operating), warnings notwithstanding. Can you isolate the reentry/static discharge effect from the dumbass-runs-engine effect?

• JF Puget

Interesting post (as usual!), but what I found most intriguing is the starting point. I reached an entirely different conclusion than yours.

You conclude “The implicit claim here is that getting in and out of my car raises my conditional probability of exploding” from “the local gas stations has a sign (pictured below) warning me to not get in and out of my car when fueling up”

My conclusion was that the conditional probability of being injured when there is a fire is smaller if you’re outside the car than if you’re inside the car. Hence being out of the car is a safer option.

Reading the rest of your post made me think that my conclusion may be wrong if going in and out of the car significantly decrease the probability of a fire. But that does not seem to be the case.

• mjb

My husband is the one who gets back in the car and leaves it running while re-fueling. I’ll let you know if he explodes.

• art2science

I like the post overall, but I think the following reasoning is dangerous:
“Any risk that happens about once every XXX fuelings is very rare. I will not fuel my car that often over the course of my lifetime, so I can expect to escape without causing a fire.”
There are a LOT of bad things that have a low probability of happening to you even over your lifetime if you indulge in them; but you still should not do them. This was brought home by an article by Jared Diamond in the NYT. A summary of the relevant point is better found here: https://www.schneier.com/blog/archives/2013/02/jared_diamond_o.html

The basic reasoning is very simple: there are MANY such activities in parallel. Suppose we regularly engage in five dangerous activities each of which has risks of roughly .001 per incident – 1 in 1000. Examples (skateboarding in traffic, sailing a small boat in a storm, standing on the top step of a ladder). But we LIKE doing them and do them regularly, say 10 times per year each, from the age of 10 to the age of 70. The total probability of being injured over your lifetime is about 95 percent!

I love to walk or jog on the beach near my office, which is directly under a 100m sandstone cliff. I have seen collapses during my visits, and every few years someone is buried by one. I check the tide level, and go somewhere else when the tide is high! I also warn off visitors sitting with their babies directly under the cliffs – teenagers and adults I leave alone.

• Matthew Saltzman

From back in 2000: http://www.cartalk.com/content/how-does-static-electricity-builds

One commenter elsewhere on the site claims that tire manufacturers have improved tires’ ability to dissipate static. There may still be some risk from static building up on the driver getting in and out of a car with cloth seats, though I don’t recall experiencing any with my last two cars. One can dissipate driver static by touching something metal with one’s key (but not near fuel vapors!).

Here’s Snopes on the phenomenon: http://www.snopes.com/autos/hazards/static.asp

One other risk that occurs to me of getting back in the car is that one is not in position to respond quickly to an accidental spill in case the auto shutoff fails or the filler neck burps.

• Laura McLay

@art2science: Thanks for your comment. I read the Jared Diamond post once upon a time. It is a nice article. Thanks for the link here, too.

You comment here is well-received. I wasn’t ignoring it in my post. Some rare risks are rarer than others (like 10^-8 or smaller). If you lumped these very rare risks together, you may be affected by any of them with a less than 1% chance over your lifetime. Different orders of magnitude. From a risk perspective, you really need to educate people about the extremely rare risks because the odds are that no one in your social network will have been affected, and it may then be unclear of how to avoid a risk. But one of my points is that we can’t really avoid the risk of exploding, at least when looking at the decision context of whether or not to go back into your car. Based on my calculations, this decision may not even affect your probability of causing an explosion. This risk is dwarfed by other risks, such as dying in a car accident. If I added other decisions to my analysis – like the decision to smoke when fueling up – then I might have to reconsider my analysis (-:

I’m glad you take care to avoid avalanches. I would, too. I also take care to avoid being struck by lightning. Some precautions are a good thing when done in moderation.

• art2science

I agree with everything in your OP, with the exception of the one sentence implying that a reasonable decision criterion is lifetime risk < ~ .5. You can validly say that I'm picking a nit, since you make clear that in this case the lifetime probability is ~1E-6. But I thought the Diamond point was one your audience would appreciate.

"Any risk that happens about once every billion fuelings is very rare. I will not fuel my car that often over the course of my lifetime, so I can expect to escape without causing a fire."

Just today I read an abstract of a paper that in London fear of terrorism after their 2011? bus bombings led people to use transport modes that were far more dangerous than the bombings themselves. (Neither one being very dangerous, of course.)

• CaptainTeknics

There exists more potential threats of fire sparks for example automobiles and static charges.

• The Other Half | Episode 2: The Road Trip

[…] And, because cars don’t run on math alone, we also consider the necessity of refueling on the road.  In particular, we ask Laura McLay to weigh in on gas station safety, as she computes the conditional probability of blowing yourself up while you’re pumping gas. […]

• Episode 2: The Road Trip | The Other Half

[…] And, because cars don’t run on math alone, we also consider the necessity of refueling on the road.  In particular, we ask Laura McLay to weigh in on gas station safety, as she computes the conditional probability of blowing yourself up while you’re pumping gas. […]