20分) F5 probability 問題一條

G = the ball is green
N = the ball is NOT green
There are 2 G and 4 N in the bag.


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Method 1 :
P(NNNN)
= [C(4,1)/C(6,1)] x [C(3,1)/C(5,1)] x [C(2,1)/C(4,1)] x [C(1,1)/C(3,1)]
= (4/6) x (3/5) x (2/4) x (1/3)
= 1/15

P(at most 4 draw)
= 1 - P(NNNN)
= 1 - (1/15)
= 14/15


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Method 2 :

P(G)
= C(2,1)/C(6,1)
= 2/6
= 1/3

P(NG)
= [C(4,1)/C(6,1)] x [C(2,1)/C(5,1)]
= (4/6) x (2/5)
= 4/15

P(NNG)
= [C(4,1)/C(6,1)] x [C(3,1)/C(5,1)] x [C(2,1)/C(4,1)]
= (4/6) x (3/5) x (2/4)
= 1/5

P(NNNG)
= [C(4,1)/C(6,1)] x [C(3,1)/C(5,1)] x [C(2,1)/C(4,1)] x [C(2,1)/C(3,1)]
= (4/6) x (3/5) x (2/4) x (2/3)
= 2/15

P(at most 4 draw)
= P(G) + P(NG) + P(NNG) + P(NNNG)
= (1/3) + (4/15) + (1/5) + (2/15)
= (5/15) + (4/15) + (3/15) + (2/15)
= 14/15

2012-03-18 22:27:22 補充：
Since 1 ball is drawn in all time, then the combination is always C(n,1) = n.

As you usually write n instead of C(n,1), it seems that the method of combination is not used.

2012-03-19 03:26:26 補充：
1. C(4,2) x C(2,1) / C(6,2) 中，分子選三個球，分母選兩個球。WhyWhyWhy你會這樣想？

2. 若果你想寫 C(4,2) x C(2,1) / C(6,3) 的話，這只是取3個球中有1個綠色的probability，不計算次序。WhyWhyWhy你會這樣想？

3. 無論是 C(4,2) x C(2,1) / C(6,2) 或 C(4,2) x C(2,1) / C(6,3)，都不等如2/5。WhyWhyWhy你會計算到2/5？