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by CrazyCatDog 580 days ago
“Knowing that 200 undersea cables break every year globally, estimate the probability that 3 cables break in the baltic sea on the same day.”

I’m stealing this to use for grad-student mock-interviews—thank you!

2 comments

Hint: The cables are often very close. If one breaks, the otherone also breaks :-)
Right, if it’s a case interview, then higher accuracy ought to prompt the interviewee to ask: (1) Do the 200 cuts typically occur in clusters? (2) What’s the typical density, eg are they usually collocated? (as an alternative to the above) (3) Are there pathways that avoid the sea but connect Europe and North America (getting at density in the sea in question) Etc.

That’s what makes this one so good—lots of opportunities to extend or roll-back difficulty.

I was surprised to see so many upvotes this morning and was disappointed when I realized it wasn't for another comment I made about the Anthropic Principle.

My take is that in face of coincidences supporting the emergence of intelligent life, we should expect to observe coincidences unnecessary for the emergence of life too.

An analogy: imagine you have lost the key to your mansion and try to cut one at random out of a metal sheet. If it can unlock the door, then chances are that you cut unnecessary notches (the analogy only holds for warded locks and the key you crafted is a master key).

See: https://news.ycombinator.com/item?id=42178306

I'm wondering where I'm wrong in my reasoning because the implication is weird.

Why would cables close to each other break?
because if it's an accident and someone is dragging an anchor behind them, if the cables are only meters apart then they are going to cut both
Wouldn't they notice after the first cable? I imagine it would be noticable
Are they?
What are the chances that they break in close proximity spacially, but not temporarily? (I'm assuming that it would be headline material if the lines had disconnected within minutes)

Tangent: an attacker trying hard to provoke that kind of accident would likely not have a very fast success feedback. "Let's try once more, for good measure"

Still pretty decent, given the right circumstances.

For example, the 2011 earthquake in Japan resulted in damage to 7 cables[0]. But it wasn't the quake itself which instantly broke all 7 cables - they were destroyed by underwater avalanches triggered by the earthquake. Avalanches can occur hours after a seismic event, and some underwater avalanches go on for days.

I highly doubt that's the case here, but if you're asking about chances it's not as unlikely as you'd think!

[0]: https://www.theverge.com/c/24070570/internet-cables-undersea...

A clever answer would be "it's a 50/50 chance, either it happens or it doesn't". That's statistics my simple brain can comprehend at least.
In what way is that clever? It's clearly wrong. If it were true, we'd experience three breakages at least 150 days of the year, every year.