Bomb Defusing in WWII

Scary stuff.
radxsays...

Well, it's still rather tricky to disarm WW2 ordinance today. Last month, a 500kg bomb killed three technicians ~90km from here. Monthly evacuations are a splendid reminder that ammunitions don't care if someone declared the war to be over.

offsetSammysays...

Scary stuff. If you do the math, let's say you had an 80% chance of successfully diffusing any given bomb. If your career consisted of diffusing only 4 bombs, and assuming an unsuccessful diffusion results in death, your chances of survival are only 40%. 6 bombs, 26%. 10 bombs, 10%. Yikes.

Note: I have no idea how accurate the 80% figure is. It would be interesting to hear the real statistic.

rychansays...

For these bombs in the middle of the road, wouldn't it be safer to just pack explosives around it, back up 100 yards, and light the fuse? Best case you tear apart the bomb and break the fuse. Worst case you set the main explosive off and do modest infrastructure damage (although less than if the bomb had simply gone off as originally intended).

Friesiansays...

My maths is pretty rusty, but I'm not sure you can do the probabilities in that manner because they're unrelated events: your success in defusing one bomb has no bearing (statistically at least) on your ability to defuse the next one. Otherwise you could say things like:

Let's imagine there's a 99% chance that the sun will rise tomorrow. Assuming the sun rises each and every day for the next two months, the "probability" it would rise on the 61st day as well is near 50/50. Take this even further, and count back to when the sun first came into existence, and it's essentially impossible that the sun would still rise tomorrow.

Don't get me wrong, bomb defusing is one hell of a risky job—hell, average life expectancy was only 10 weeks according to the video—but I don't think your probabilities hold up.>> ^offsetSammy:

Scary stuff. If you do the math, let's say you had an 80% chance of successfully diffusing any given bomb. If your career consisted of diffusing only 4 bombs, and assuming an unsuccessful diffusion results in death, your chances of survival are only 40%. 6 bombs, 26%. 10 bombs, 10%. Yikes.
Note: I have no idea how accurate the 80% figure is. It would be interesting to hear the real statistic.

offsetSammysays...

You are correct that each bomb diffusion is an independent event and always has the same probability of success, but it is also correct to say that the chances of successfully diffusing 4 bombs IN A ROW is 40%, 10 bombs IN A ROW is 10%, etc. In this case each event is dependent, but you have to work out the probabilities at the start, before any bombs are diffused.

It's kind of like flipping a coin (which has a 50% chance of landing heads or tails every time). Every time I flip it, I have a 50% chance of landing on heads, but my chances of getting say 5 heads in a row is only 3%. (0.5^5) Imagine that flipping tails results in death. Now you can start to see the peril these guys were in!

So if the 80% bomb diffusion success rate was correct, it would be valid to say, BEFORE the person does it, that if they are tasked with diffusing 10 bombs, their chances of survival are only 10%. Note that, every time they successfully diffuse a bomb, their overall odds of survival improve a little bit (because now they only have to diffuse 9 in a row, 8 in a row, etc).

p.s. I think you'll find that the chance of the sun rising every day is quite a bit higher than 99%.

>> ^Friesian:

My maths is pretty rusty, but I'm not sure you can do the probabilities in that manner because they're unrelated events: your success in defusing one bomb has no bearing (statistically at least) on your ability to defuse the next one. Otherwise you could say things like:
Let's imagine there's a 99% chance that the sun will rise tomorrow. Assuming the sun rises each and every day for the next two months, the "probability" it would rise on the 61st day as well is near 50/50. Take this even further, and count back to when the sun first came into existence, and it's essentially impossible that the sun would still rise tomorrow.
Don't get me wrong, bomb defusing is one hell of a risky job—hell, average life expectancy was only 10 weeks according to the video—but I don't think your probabilities hold up.>> ^offsetSammy:
Scary stuff. If you do the math, let's say you had an 80% chance of successfully diffusing any given bomb. If your career consisted of diffusing only 4 bombs, and assuming an unsuccessful diffusion results in death, your chances of survival are only 40%. 6 bombs, 26%. 10 bombs, 10%. Yikes.
Note: I have no idea how accurate the 80% figure is. It would be interesting to hear the real statistic.


Friesiansays...

>> ^offsetSammy:

You are correct that each bomb diffusion is an independent event and always has the same probability of success, but it is also correct to say that the chances of successfully diffusing 4 bombs IN A ROW is 40%, 10 bombs IN A ROW is 10%, etc. In this case each event is dependent, but you have to work out the probabilities at the start, before any bombs are diffused.
It's kind of like flipping a coin (which has a 50% chance of landing heads or tails every time). Every time I flip it, I have a 50% chance of landing on heads, but my chances of getting say 5 heads in a row is only 3%. (0.5^5) Imagine that flipping tails results in death. Now you can start to see the peril these guys were in!
So if the 80% bomb diffusion success rate was correct, it would be valid to say, BEFORE the person does it, that if they are tasked with diffusing 10 bombs, their chances of survival are only 10%. Note that, every time they successfully diffuse a bomb, their overall odds of survival improve a little bit (because now they only have to diffuse 9 in a row, 8 in a row, etc).
p.s. I think you'll find that the chance of the sun rising every day is quite a bit higher than 99%.
>> ^Friesian:
My maths is pretty rusty, but I'm not sure you can do the probabilities in that manner because they're unrelated events: your success in defusing one bomb has no bearing (statistically at least) on your ability to defuse the next one. Otherwise you could say things like:
Let's imagine there's a 99% chance that the sun will rise tomorrow. Assuming the sun rises each and every day for the next two months, the "probability" it would rise on the 61st day as well is near 50/50. Take this even further, and count back to when the sun first came into existence, and it's essentially impossible that the sun would still rise tomorrow.
Don't get me wrong, bomb defusing is one hell of a risky job—hell, average life expectancy was only 10 weeks according to the video—but I don't think your probabilities hold up.>> ^offsetSammy:
Scary stuff. If you do the math, let's say you had an 80% chance of successfully diffusing any given bomb. If your career consisted of diffusing only 4 bombs, and assuming an unsuccessful diffusion results in death, your chances of survival are only 40%. 6 bombs, 26%. 10 bombs, 10%. Yikes.
Note: I have no idea how accurate the 80% figure is. It would be interesting to hear the real statistic.



Yeah, I was thinking along the same lines, but there's something about it which makes me sit back and question it.


Interestingly, 3% seems really really low for getting 5 heads in a row (oh, I know it's correct, but it just appears low). There are 2 to the power 5 different combinations of heads/tails from 5 coin flips (32). As you've got to have at least one combination, 100%/32 (as they're all just as likely) = 3.125%, which is the same as 1/2 * 1/2 * 1/2 * 1/2 * 1/2. I know I'm just reiterating what you said, but this helps me get it through my skull and into my brain.

Perhaps I'm overthinking this, or maybe ever since I heard about the Monty Hall problem I've never trusted myself to be able to accurately figure out probabilities.

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