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1. 
可能
ke3 neng2
Adv. From previous classes, you may have already known the characters 可 and 能. Both characters can mean 'capability' and 'possibility' individually. When put together, the word they make up of always means probability/chance/possibility.
In a sentence, 可能 is put ahead of "verb (+ noun)" structure, just like "May" in English.
See the following example:
2. 他 可能 喜欢 数学
ta1 ke3neng2 xi3huan1 shu4xue2
He perhaps/may likes math.
3. 我 可能 很快 辞职
wo3 ke3neng2 hen3kuai4 ci2zhi2
I may soon quit (my job).
4. 不 可能
bu4 ke3 neng2
"cannot, improbable to, unlikely to".
Here, 不 is put ahead of 可能. It means the situation/action that follows is very unlikely happen. The negative sense is used toward to '可能' likelihood. This is different from the case when 不 is put behind 可能, which will be explain later in this class.
5. 她 不可能 有 三十岁
ta1 bu4ke3neng2 you3 san1shi2sui4
She cannot be 30 years old.
6. 我们 不可能 忘记 这场 比赛
wuo3men2 bu4ke3neng2 wang4ji4 zhe4chang3 bi3sai4
We can never forget this game.
7. 可能不
ke3neng2 bu4
May not, perhaps not
Compared with 不可能 in point 4, 不 is put behind 可能. It means the situation/action that follows is likely to happen in negative sens. The negative sense is used toward to the situation/action rather than '可能' likelihood.
8. 她 可能 没有 三十岁
ta1 ke3neng2 mei2you3 san1shi2sui4
She may not be 30 years old.
*Compared with point 5., it shows a less degree of certainty because, again, negative sense is used toward ‘有’ not ‘可能’.
9. 我们 可能 不会 忘记 这场 比赛
wuo3men2 ke3neng2 bu2hui4 wang4ji4 zhe4chang3 bi3sai4
We may not forget this game.
