高一几何概率题
问题描述：
高一几何概率题
任取m∈[-2,5],n∈[-3,1],则关于x的一次函数y＝(m-n)x＋5是增函数的概率为?
答
The answer is 47/56.
The function y is increasing if and only if m>=n.
If m>=1, then m>=n for any n. This contributes (5-1)/(5-(-2))=4/7.
Otherwise -2In this case, if -3=n for all m. This contributes
(1-(-2))/(5-(-2)) * (-2-(-3))/(1-(-3)) = 3/7 * 1/4.
Otherwise both m and n are in the interval [-2,1]. This contributes
3/7 * 3/4 * 1/2.
Hence the total probability of m>=n is
4/7+3/7*(1/4+3/4*1/2)=47/56.it can not m＝nm=n�ǿ��Եġ�ͨ����������Ķ����У���������һ���������������˵��m>n�ĺ������ֽС��ϸ����������Ҫ��f���ϸ�������ĸ��ʣ������m=n�ĸ��ʼ��ɣ�Ҳ���Ǽ���0������Ϊ47/56.