题目内容
集合A={x|x2-3x-10<0,x∈Z},从集合A中任取两个元素a、b且a·b≠0,则方程
=1表示焦点在x轴上的椭圆的概率为________.
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A={x|-2<x<5,x∈Z}={-1,0,1,2,3,4},由条件知,(a,b)的所有可能取法有:(-1,1),(-1,2),(-1,3),(-1,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(1,-1),(2,-1),(3,-1),(4,-1),(2,1),(3,1),(4,1),(3,2),(4,2),(4,3),共20种,方程
=1表示焦点在x轴上的椭圆,应有a>b>0,∴有(2,1),(3,1),(4,1),(3,2),(4,2),(4,3)共6种,∴ 所求概率P=
=
.
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