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標題: 中五概率求教 [打印本頁]

作者: kinrex721 時間: 2011-5-9 05:33 PM 標題: 中五概率求教

引用:

Question:

Bag A contains 7 red balls and 5 blue balls.
Bag B contains 5 red balls and 4 green balls.
One ball is randomly drawn from A and put into B.
Then one ball is drawn from bag B randomly and put into A.
Final, a ball is drawn from A at random.

Find the probability that the final ball drawn from bag A is
(i) Red
(ii) Blue
(iii) Green

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小弟用左好耐時間先計到紅波概率=(93/160), 藍波概率=(37/96)!

所以想起到問下有冇咩快D嘅方法可以計到? 仲有我個紅波藍波答案岩唔岩?

綠波概率係咪可以=(1-P(Red)-P(Blue))? 求教求教, 萬分感謝!

作者: ryan1203 時間: 2011-5-9 06:09 PM

引用:

原帖由 kinrex721 於 2011-5-9 05:33 PM 發表

-

小弟用左好耐時間先計到紅波概率=(93/160), 藍波概率=(37/96)!

所以想起到問下有冇咩快D嘅方法可以計到? 仲有我個紅波藍波答案岩唔岩?

綠波概率係咪可以=(1-P(Red)-P(Blue))? ...

i. (7/12)[(6/10)(7/12) + (4/10)(6/12)] + (5/12)[(5/10)(8/12) + (5/10)(7/12)] = 349/480?(禁錯計數機

,93/160先岩)

ii. (7/12)(5/12) + (5/12)[(1/10)(5/12) + (9/10)(4/12)] = 37/96(果然畫個diagram係好d

)

iii. 1 - P(red) - P(blue)

[ 本帖最後由 ryan1203 於 2011-5-9 06:43 PM 編輯 ]

作者: hinokari 時間: 2011-5-9 06:27 PM

.....

作者: hinokari 時間: 2011-5-9 06:32 PM

P(R)=(7/12)[(6/10)(7/12)+(4/10)(6/12)]+(5/12)[(5/10)(8/12)+(4/10)(7/12)+(1/10)(7/12)]
=93/160
P(B)=(7/12)(6/10+4/10)(5/12)+(5/12)[(5/10+4/10)(4/12)+(1/10)(5/12)]
=37/96
P(G)=1-P(R)-P(B)=1/30

To Solve these Problem,Tree diagram is a GREAT Technique.
Count the ball in each bag in each case and write down once,
then you can operate "+" or "x" to solve all answer you want.

[ 本帖最後由 hinokari 於 2011-5-9 06:33 PM 編輯 ]

作者: kinrex721 時間: 2011-5-9 06:42 PM

引用:

原帖由 hinokari 於 2011-5-9 06:32 PM 發表
P(R)=(7/12)[(6/10)(7/12)+(4/10)(6/12)]+(5/12)[(5/10)(8/12)+(4/10)(7/12)+(1/10)(7/12)]
=93/160
P(B)=(7/12)(6/10+4/10)(5/12)+(5/12)[(5/10+4/10)(4/12)+(1/10)(5/12)]
=37/96
P(G)=1-P(R)-P(B)=1/30

To ...

上面幅圖幫助好大, 感謝賜教!

作者: hinokari 時間: 2011-5-9 06:57 PM

到時就係你Construct 依幅圖gala....

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