Question

请教一道概率题，问题如下。

Suppose that n independent trials, each of which results in any
of the outcomes 0, 1, or 2, with respective probabilities p0, p1, and p2,
p0+p1+p2=1, are performed. Find the probability that outcomes1 and 2 both
occur at least once.

Answer 1

分三种情况,①1和2中只有1发生 0随便它 则p1(1-p2)
②1和2中只有2发生 则p2(1-p1)
③1和2都发生 则p1*p2
三个相加 根据p0+p1+p2=1代入,得所求概率P=1-p0-p1*p2