Question

袋中有2n-1个白球和2n个黑球,今随机不放回抽取n个,发现它们是同色的,求同为黑色的概率

Answer 1

C(2n,n)/(C(2n,n)+C(2n-1,n))

=1÷(1+C(2n-1,n)/C(2n,n))

=1÷(1+((2n-1)!/(n-1)!)/((2n)!/n!))

=1÷(1+n/(2n))

=1÷(1+1/2)

=1÷(3/2)

=2/3