设集合P={b,1},Q={c,1,2},P⊆Q,若b,c∈{2,3,4,5,6,7,8,9}. (1)求b=c的

设集合P{b,1}Q{c,1,2}PQ,若bc∈{2,3,4,5,6,7,8,9}

(1)bc的概率;

(2)求方程x2bxc0有实根的概率.

答案

解:(1)因为PQ,当b2时,c3,4,5,6,7,8,9;当b2时,

bc3,4,5,6,7,8,9,基本事件总数为14.其中bc的事件数为7种,所以bc的概率为:.

(2)方程有实根为事件A,若使方程有实根,则Δb24c≥0,即bc4,5,6,7,8,96. 所以P(A).

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