prep一道概率题，怎么解呀？

The figuer shown represents a board with four rows of pegs, and at the bottom of the board are four cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hig the peg directly beneath the opening. The ball then has probability of 1/2 of passing through the opening immediately to the left of the peg and probability of 1/2 of passing though 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 up in cell 2.

我画得不好，但基本就这个样子。O is the ball, and 0 is peg.

                                                          O

                                                       0     0

                                                    0     0     0

                                                 0     0     0     0

                                              0    0      0     0     0

                                              I-----i-----i-----i-----i

                                                 1     2     3    4

图变形了，应该是这样。

                                  O

                                0   0

                              0   0   0

                            0   0   0   0

                          0   0   0   0   0

                          i----i----i----i----i  

answer: 3/8

一共有2*2*2条路，其中转向为“左左右”，“左右左”，“右左左”的进入2号牢房

可以画一下~

终于想明白了，mm的数学真强悍呀。谢谢。