數學問題（ｐｒｏｂａｂｉｌｉｔｙ）

１．
(a)(I) P( Two white balls )
= 3/7 x 2/6 .....FIRST time take white ball ,the bag remain 6 balls(include white ball)
= 6/42
= 1/7

(ii)P( Two balls of the same colour) .....mean 2R + 2B + 2W
= 2/7 x 1/6 + 2/7 x 1/6 + 3/7 x 2/6 .....OR 2/7 x 1/6 x 2 + 3/7 x 2/6
= 2/42 + 2/42 + 6/42
= 10/42
= 5/21

III)P( One black ball and one white ball )
= 2/7 x 3/6 + 3/7 x 2/6 .....OR 2/7 x 3/2 x 2
= 6/42
= 1/7


2008-01-24 23:27:47 補充：
III) 解釋 : 第一次拿左白 ,第二次就要拿黑 ;第一次拿黑 ,第二次就一定要拿白

2008-01-24 23:30:21 補充：
sorryIII)個步驟同答案錯左 ,但條式冇錯III)P( One black ball and one white ball )= 2/7 x 3/6 3/7 x 2/6 = 6/42 6/42= 2/7

2008-01-24 23:30:50 補充：
= 6/42 6/42= 2/7

2008-01-24 23:31:23 補充：
= 6/42 + 6/42= 2/7

1. (3/7)(2/6)=1/7
2. (2/7)(1/6)+(2/7)(1/6)+(3/7)(2/6)=5/21
3. 2(2/7)(3/6)=2/7

ai) probability of draw 2 white balls is
(3/7) x (2/6)
=1/7
aii) probability of draw 2 balls in same colour is
= probability of draw 2 red + probability of draw 2 blue +probability of draw 2 white
= (2/7) x (1/6) + (2/7) x (1/6) + 1/7 (from ai)
= 5/21
aiii) probability of draw 1 black 1 white
= probability of draw a black then a white + probability of draw a white then a black
= (2/7) x (3/6) + (3/7) x (2/6)
= 2/7