将一枚质地均匀的骰子连掷两次，记向上的点数分别为a，b．（Ⅰ）求事件“a+b=8”的概率；（Ⅱ）求事件“ 将一枚质地均匀的骰子连掷两次，记向上的点数分别为a，b．（Ⅰ...
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\uff08\u2160\uff09\u7531\u9898\u610f\u5f97\uff0c\u63b7\u9ab0\u5b501\u6b21\uff0c\u5176\u5411\u4e0a\u7684\u70b9\u6570\u67096\u79cd\u60c5\u51b5\uff0c\u5219\u5c06\u4e00\u679a\u9ab0\u5b50\u8fde\u63b7\u4e24\u6b21\uff0c\u57fa\u672c\u4e8b\u4ef6\u7684\u603b\u4e2a\u6570\u662f6\u00d76=36\uff0c\u5373\uff08a\uff0cb\uff09\u7684\u60c5\u51b5\u670936\u79cd\uff0c\u4e8b\u4ef6\u201ca+b=8\u201d\u5305\u542b\u57fa\u672c\u4e8b\u4ef6\uff1a\uff082\uff0c6\uff09\uff0c\uff083\uff0c5\uff09\uff0c\uff084\uff0c4\uff09\uff0c\uff085\uff0c3\uff09\uff0c\uff086\uff0c2\uff09\uff0c\u51715\u4e2a\uff0c\u2234\u6240\u6c42\u4e8b\u4ef6\u7684\u6982\u7387\u4e3a536\uff0e\u3000\uff08\u2161\uff09\u82e5\u65b9\u7a0bax2+bx+1=0\u6709\u5b9e\u6839\uff0c\u5219\u5fc5\u6709\u25b3=b2-4a\u22650\uff0c\u82e5a=1\uff0c\u5219b=2\uff0c3\uff0c4\uff0c5\uff0c6\uff0c\u82e5a=2\uff0c\u5219b=3\uff0c4\uff0c5\uff0c6\uff0c\u82e5a=3\uff0c\u5219b=4\uff0c5\uff0c6\uff0c\u82e5a=4\uff0c\u5219b=4\uff0c5\uff0c6\uff0c\u82e5a=5\uff0c\u5219b=5\uff0c6\uff0c\u82e5a=6\uff0c\u5219b=5\uff0c6\uff0c\u2234\u4e8b\u4ef6\u201c\u65b9\u7a0bax2+bx+1=0\u6709\u5b9e\u6839\u201d\u5305\u542b\u57fa\u672c\u4e8b\u4ef6\u51715+4+3+3+2+2=19\u4e2a\uff0c\u2234\u6240\u6c42\u4e8b\u4ef6\u7684\u6982\u7387\u4e3a1936\uff0e
| 解：（Ⅰ）由题意得，掷骰子1次，其向上的点数有6种情况， 则将一枚骰子连掷两次，基本事件的总个数是6×6=36， 即（a，b）的情况有36种，事件“a+b=8”包含基本事件：（2，6），（3，5），（4，4），（5，3），（6，2），共5个， ∴所求事件的概率为 ． （Ⅱ）若方程ax 2 +bx+1=0有实根，则必有△=b 2 ﹣4a≥0， 若a=1，则b=2，3，4，5，6， 若a=2，则b=3，4，5，6， 若a=3，则b=4，5，6， 若a=4，则b=4，5，6， 若a=5，则b=5，6， 若a=6，则b=5，6， ∴事件“方程ax 2 +bx+1=0有实根”包含基本事件共5+4+3+3+2+2=19个， ∴所求事件的概率为 ． |
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