I never learned about molecular biology or transistors at school, but genetic engineering and computers are two of the developments most likely to change the way we live in the future.

什么情况下副词短语作后置定语，其关系代词that/which 可省略？如这道题的粗体字"most likely..." 前省略了that/which。

这个句子你理解错了：

likely是形容词，不是副词。likely后接不定式构成形容词短语，作后置定语。相当于一个定语从句省略了关系代词that/which和系动词被。例如：

Tom is likely to win.

=It is likely that Tom will win.

the develoments most likely to change...

=the developments which are most likely to change...

（顺便解释一下the way后面的定语从句。如果关系词在从句中作方式状语，用关系副词that引导，这个that也可以省略。也可以用in which引导。用that或省略that为非正式语体，用in which则显得正式一些。

that作为关系副词引导定语从句属于非正式语体，先行词可以是时间名词，the reason, the place, the way. 这个that可以省略。因此它可以代替when, why, where, in which. that的使用和先行词有关，不可滥用。正式语体也很少用。)