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第295题是不是这样的,从GWD找到的(不过我不会贴图):
The figure shown represents a board with 4 rows of pegs, and at the bottom of the board are 4 cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has the probability of passing through the opening immediately to the left of that peg and probability of passing through the opening immediately to the right. What is the probability that when the ball passes through the first two pegs at the top it will end in Cell 2? A.1/16 B.1/8 C.1/4 D.3/8 E.1/2 正确答案D
解释: 球是从正中间那掉下来的,而地下四个数字表示对应最后一行的四个洞洞,因此第一次(只有两个黑点组成一个洞的)掉落没有概率之说,反正只能从这唯一入口进来,接下来第二行(三个黑点)分别概率为1/2和1/2,第三行(有四个黑点三个洞洞)每个洞洞的概率分别是1/2*1/2,1/2*1/2+1/2*1/2,1/2*1/2即1/4,2/4,1/4(因为中间的洞洞有更大的可能性因为两边都可以掉下来),第四行(有五个黑点四个洞洞)每个洞洞概率算法同第三行一样分别是1/4*1/2,1/4*1/2+2/4*1/2,1/4*1/2+2/4*1/2,1/4*1/2即1/8,3/8,3/8,1/8,数字2对应的洞洞为第二个所以概率为3/8. |
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