1 . 考查等式:
(*),其中
,
且
.某同学用概率论方法证明等式(*)如下:设一批产品共有
件,其中
件是次品,其余为正品.现从中随机取出
件产品,记事件
{取到的
件产品中恰有
件次品},则
,
,1,2,…,
.显然
,
,…,
为互斥事件,且
(必然事件),因此
,所以
,即等式(*)成立.对此,有的同学认为上述证明是正确的,体现了偶然性与必然性的统一;但有的同学对上述证明方法的科学性与严谨性提出质疑.现有以下四个判断:①等式(*)成立,②等式(*)不成立,③证明正确,④证明不正确,试写出所有正确判断的序号___________ .
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