数学可能性：掷2个6面骰子两次,两次总和相同的几率是多少?如题,请写过程.

Question

数学可能性：掷2个6面骰子两次,两次总和相同的几率是多少?
如题,请写过程.

Answer 1

掷2个6面骰子,共有以下36种等可能的情形,每1种情形出现的概率都是1/36：
{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}.
它们的点数之和分别是：
2,3,4,5,6,7,
3,4,5,6,7,8,
4,5,6,7,8,9,
5,6,7,8,9,10,
6,7,8,9,10,11,
7,8,9,10,11,12.
从小到大排序后是：
2,
3,3,
4,4,4,
5,5,5,5,
6,6,6,6,6,
7,7,7,7,7,7,
8,8,8,8,8,
9,9,9,9,
10,10,10,
11,11,
12.
它们出现的概率(也就是掷2个6面骰子,总和为以下点数的概率)分别是：
2:1/36,
3:2/36,
4:3/36,
5:4/36,
6:5/36,
7:6/36,
8:5/36,
9:4/36,
10:3/36,
11:2/36,
12:1/36.
掷2个6面骰子两次,两次总和同为以下点数的概率是：
2:(1/36)^2= 1/1296,
3:(2/36)^2= 4/1296,
4:(3/36)^2= 9/1296,
5:(4/36)^2=16/1296,
6:(5/36)^2=25/1296,
7:(6/36)^2=36/1296,
8:(5/36)^2=25/1296,
9:(4/36)^2=16/1296,
10:(3/36)^2= 9/1296,
11:(2/36)^2= 4/1296,
12:(1/36)^2= 1/1296.
所以,掷2个6面骰子两次,两次总和相同的概率就是以上数值相加：
146/1296=73/648.