F.3 MATH (Introduction of Probability) 10分

首先，要找出有多少個組合是 the difference is larger than 2:
1. 要搞清楚一點，就是這只是抽兩個數，故此，組合(1,6) 和 組合(6,1)是沒有分別的。
the difference is larger than 2 有 6組:
1 6
1 5
1 4
2 6
2 5
3 6

接著，要找出總共有多少個組合︰
如果對combination有認識，可以用 6C2=(6*5)/(2*1)=15
如果對combination沒有認識，就唯有 用列舉的方法了 ︰ (也可以數到15組)
1 2
1 3
1 4
1 5
1 6
2 3
2 4
2 5
2 6
3 4
3 5
3 6
4 5
4 6
5 6

故此，答案是 6/15 = 2/5

The sample space of the probability of the two numbers are larger than 2:
{(1,4),(1,5),(1,6),(4,1),(5,1),(6,1),(2,5),(3,6),(5,2),(6,3),(3,6)}
There is totally 11 combinations that the difference of the numbers chosen are larger than 2.
And there is totally 4x5=20 combinations of two numbers taken.
Therefore the P(the difference of the numbers chosen is larger than 2)
=11/20=0.55

2007-03-05 22:01:15 補充：
我認為(1,6)與(6,1)是有分別的正如擲硬幣公字與字公是有分別的因為這已是兩種擲法因此,(1,6)與(6,1)是有兩種機會抽到的

1) If teo numbers are taken from 1, 2, 3, 4, 5, and 6 at random, find the probability that

the difference is larger than 2.

the chance that the difference larger than 2

1,6
1,5
1,4
2,6
2,5
3,6

so,the probability is

(1/6)^2 x 6 x 2

= 1/3

2007-03-05 20:27:43 補充：
the probability should be 1/6 x 1/5 x 12= 2/5