At the risk of their lives they had driven to desert, recovered many women and children, and brought them back to the camp.

I would have written it this way:
In spite of the risk to their lives they had driven to desert...

I can't take the risk of being killed. Can't take the "risk of" what? Of being killed.

"At" is a preposition here and "of" is also a preposition close in meaning to 'about'. Would you please help to understand the structure "At the risk of their lives"?
"At the risk of their lives they had done x" is perfectly idiomatic.

I would say, "into the desert."

Your other uses of "risk" are also okay.

"You are at risk here." I'd say "at risk" is an idiom. "At the risk of" is probably another (related) one.

Do you have it listed at the end of your noun entry for "risk"?

Enter at your own risk!

You do this at your own peril.

I took this trip at my own expense.
Thanks, Avangi.
AvangiDo you have it listed at the end of your noun entry for "risk"?
Yes, M-W has it.

at risk

: in a state or condition marked by a high level of risk or susceptibility <patients at risk of infection>

[M-W col. Dic.]

I'm using the dictionary a little less these days, I have to say.

Even then it doesn't really click with me. I would have said: At the risk of danger to their lives they drove into the desert.

Please guide.
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"Risk of danger" is redundant, isn't it?

How much money are you willing to risk on this deal? You're putting your money in danger.
You're putting it at risk.

To risk X is to put X in danger.

I risked the lives of my family by driving drunk.

Yes, you can double it up if you want:
I risked exposing my family to danger. Maybe you could call this a nested risk. Emotion: big smile

This perhaps means that you didn't really expose them to danger, but there was a chance you might have.
This is like wearing both a belt and suspenders.

"I risked their lives by exposing them to danger" is redundant, in a certain sense of the word.
"to risk", 'risk' functioning as a verb. "at risk or at the risk" - 'risk' is a noun.

"He loved her so much that he went to see her even at the risk of infection."
"He risked his health to see her while she was suffering from an extremely infectious disease."

I don't know where I'm going wrong. Please guide.

BTW, what's that "nested risk"? Perhaps, it's a nested risk when there is a chance that you would survive it even though this equally probable you could also be harmed in some way.

Thanks for all the help.
I think you have the idea.

I "made up" the "nested risk" - a risk embedded within a risk. (You're a programmer, right?)

Are you still unhappy with some of the phrases? - Which?


Re the article for "desert," it works like the ocean, or the sky:

From this vantage point, all I can see is ocean/desert/sky.

Right now, I'm looking at the ocean/desert/sky.

Let's go to the ocean/desert!

You can lead a horse to water. (no article)

The animal went to ground. (idiom - no article)

In the first two examples, the article is optional. Without the article, it's definitely uncountable.
We went to a desert. We went to an ocean. These are definitely countable.
We went to the desert. We went to the ocean. These are something else.
They had driven to desert country. (no article. "Desert" is an adjective.)
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Hi Avangi

1: At the risk of their lives they had driven into the desert.
2: In this hospital patients are at risk of further infection.

at risk - possibility of loss or injury

Both "of's" are presposition but for some reason I think they stand for different definition of "of" in each sentence.

of (preposition):

For #1 5a or 9a seems fitting. And 2b would go in #2.

And these article issue which we also touched here:

I would get back to this discussion some time in near future, I hope so.

Thanks a lot.