问题 填空题

将一枚骰子抛掷两次,若先后出现的点数分别为b,c,则方程x2+bx+c=0有实根的概率为 ______.

答案

将一枚骰子抛掷两次,若先后出现的点数分别为b,c,共有36种结果:(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6),属于古典概率模型.

记“方程x2+bx+c=0有实根”为事件A,则△=b2-4c≥0⇒b≥2

c
,A包含的结果有:(2,1)(3,1)(4,1)(5,1)(6,1)(3,2)(4,2)(5,2)(6,2)(4,3)(5,3)(6,3)(4,4)(5,4)(6,4)(5,5)(6,5)(5,6)(6,6)共19种结果,由古典概率的计算公式可得,P(A)=
19
36

故答案为:

19
36

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