Re: [機統] 一題黑球與白球的問題

看板Math作者cuttlefish (無聊ing ><^> .o O)時間13年前 (2012/05/29 01:42)推噓2(2推 0噓 7→)

留言9則, 3人參與討論串2/2 (看更多)

※ 引述《gn01349943 (flying)》之銘言： : 這題想了很久，就是沒什麼頭緒，不知道有沒有什麼關鍵呢? : A box contains p white balls and q black balls. Beside the box there is a pile : of black balls. Two balls are taken out from the box. If they are of the same : color, a black ball from the pile is put in the box. If they are of different : colors, the white ball is put back into the box. This procedure is repeated : until the last pair of balls is removed from the box and one last ball is put : in. What is the probability that this last ball is white? : 我的想法是，這題等於是要求最後盒子裡剩下一黑一白的機率? : 可是當這樣想時，感覺只有一步一步列舉的方法，不知道有沒有更好的想法呢？ : 謝謝大家! 每次動作都會少一顆球目前有p+q顆所以最後剩1顆共經過了p+q-1次設x,y,z分別是其中每次拿出2顆球為黑黑,白白,黑白的次數有關係式: x+y+z = p+q-1 p-2y = 1 q-x+y-z = 0 (1) p為奇數: Prob = 0 (2) p為偶數: y = (p-1)/2 , x + z = q + (p-1)/2 (= q + y ) 注意到x及z的次數不重要所以需考慮的只有 P(白白)=1/4 及 P(非白白)= 3/4 的二項式分配機率 = C(p+q-1,y) * (1/4)^y * (3/4)^(q+y) -- ^^ ('') ~我是可愛的兔子 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 123.193.28.199

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gn01349943

05/29 02:26, , 1^F

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LPH66

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LPH66

05/29 09:06, , 3^F

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