同時(shí)拋擲兩枚均勻的骰子,骰子個(gè)面上的點(diǎn)數(shù)分別是1、2、…、6拋出的點(diǎn)數(shù)之和為x,概率為p.
(1)當(dāng)
p=時(shí),求x值.
(2)若將所有的x,p記作點(diǎn)(x,p),則有11個(gè)點(diǎn),這些點(diǎn)是否關(guān)于某一直線對(duì)稱?若對(duì)稱,寫(xiě)出對(duì)稱軸方程.
(3)這些點(diǎn)是否在同一拋物線上:______(填“是”或“否”).
(1)列表得:
(1,6) | (2,6) | (3,6) | (4,6) | (5,6) | (6,6) |
(1,5) | (2,5) | (3,5) | (4,5) | (5,5) | (6,5) |
(1,4) | (2,4) | (3,4) | (4,4) | (5,4) | (6,4) |
(1,3) | (2,3) | (3,3) | (4,3) | (5,3) | (6,3) |
(1,2) | (2,2) | (3,2) | (4,2) | (5,2) | (6,2) |
(1,1) | (2,1) | (3,1) | (4,1) | (5,1) | (6,1) |
∵共有36種情況,只有出現(xiàn)3種情形時(shí),p=
.
∴x=4或x=10.(5分)
(2)11個(gè)點(diǎn)分別是
(2,),
(3,),
(4,),
(5,),
(6,),
(7,),
(8,),
(9,),
(10,),
(11,),
(12,).
它們關(guān)于某一直線對(duì)稱,對(duì)稱軸方程是x=7.(10分)
(3)設(shè)在拋物線y=a(x-7)
2+
上,
代入點(diǎn)(2,
),得:a=-
;
代入點(diǎn)(3,
),得:a=-
;
可得這些點(diǎn)不在同一拋物線上.
故答案為:否.(12分)