probability

the questions can be change to find the P of all the three number are the same, i think you can find it very easily, don't you?
so P(the three number are different)+P(the three number are the same)=1


the product of the three number is either odd or even, so the result is half and half ie 0.5

2006-10-19 23:03:47 補充：
1- (1/6)X(1/6)X(1/6) X6=35/36

三粒要唔同，所以第一粒係乜都冇所謂，第二、三粒先係要concern的事
第二粒要同第一粒唔同=5/6
第三粒要同前兩粒唔同=4/6
所以三粒唔同的機會=5/6*4/6=20/36=5/9

三粒乘埋係雙數，即係唔好三粒係單數
所以=1-1/2*1/2*1/2=7/8

three numbers are different:
first die: 咩結果都冇所課
second die: 要同第一粒既結果唔同，即only 5 options
third die: 要同第一、二粒既結果唔同，即only 4 options
P(three numbers are different)
= 1 x 5/6 x 4/6
= 20/36
= 5/9

product of the three numbers is even
只要其中一粒係even，個product就自然係even
only 1 die is even: ooe, oeo, eoo
only 2 dice are even: oee, eoe, eeo
3 dice are even: eee
P(product of the three is even)
= (1/2)^3 x 3 + (1/2)^3 x 3 + (1/2)^3
=7/8

2006-10-19 23:49:10 補充：
three numbers are different:first die: 咩結果都冇所謂 (打錯字)

P(the three number are different)

There are 6 no. of result will get if you throw a dice. Therefore if 3 dice are thrown, the no. of result = 6 x 6 x 6

∴P(the three number are different)
=P(96)
=96/216
=4/9 (four over nine)




There are only 2,2,2. , 4,4,4. & 6,6,6. three result will make the product of the three number is even.

P(the product of the three number is even)
=P(3)
=3/216
=1/72

2006-10-19 23:44:27 補充：
sorry,I correct part 2 as：If there is one or about dice show an even no,then the product must be even.Only1,3,5 is odd no, and only if the 3 no. of the 3 dice are odd no. can not get the their product to even.∴ The product of the three number is even=216- (3x3x3)=189P(189)=189/216=7/8

a) 5/9

b) 1/2