请教老师这个句子：

People exploited all the possibilities of improving their life standards

解答如下

上面的介词短语作possibilities的定语，不可以改成不定式,但是可以改为同位语从句.如下

People exploited all the possibilities that they would improve their life standards

解答如下

possibility后不能接动词不定式,但可以可接“of sth/ doing”结构或that同位语从句。

(1)possibility of doing sth 做某事的可能性

There is one possibility of changing jobs.
换工作是有可能的事。

(2)possibility of sth 某事的可能性

She saw the possibilities of the scheme from the beginning.
她从一开始就预见到这计划可能成功。

(3)possibility that 同位语从句

We must accept the possibility that we might be wrong.
我们必须承认，我们有可能搞错了。

possibility that 同位语从句

Is there any possibility that you'll be back by the weekend?
周末以前你有可能回来吗?

We were not in the least worried about the possibility that sweets could rot the teeth.

我们以前完全不担心吃糖果有可能会蛀牙。

We can't exclude the possibility that it will rain.

我们不能排除天会下雨的可能性。