Strategy

If it shows tail, switch coin, until you get a head, then keep using this coin forever.
The idea to find the prob*****ility is to consider different cases:
1. the first toss is a head (the probability os which is 1/4)
2. getting the first head on second toss (prob = (3/4)*(1/4))
3. getting the first head on third too (prob = (3/4)*(3/4)*(1/4))
and so on,...

The above cases will give you different positions on ladder when you are sure you have the fair coin, from this moment you start a random walk up and down with the same probability.

所有跟帖： 

• 回复：Strategy -Commentate- ♂ (64 bytes) () 07/17/2009 postreply 10:23:02

• If there are m steps up and n steps down -屋漏痕- ♂ (61 bytes) () 07/17/2009 postreply 10:55:12

• Cool, then we are done! -Commentate- ♂ (0 bytes) () 07/17/2009 postreply 11:24:38

• What about the chance of staying on the ladder? -dayuwang- ♂ (0 bytes) () 07/17/2009 postreply 12:29:09

• 0... if one keeps walking. -屋漏痕- ♂ (0 bytes) () 07/17/2009 postreply 12:50:45

• 回复：What about the chance of staying on the ladder? -crazy_math- ♂ (133 bytes) () 08/07/2009 postreply 02:22:02

• 差不多就是这样 -康MM- ♀ (52 bytes) () 07/17/2009 postreply 17:19:34

• 这样的考官挺折磨人。胆小的人碰上就倒霉了：）不过你倒给提了个好醒。谢谢！ -戏雨飞鹰- ♀ (0 bytes) () 07/18/2009 postreply 07:26:42

• 回复：Strategy -雪山飞鱼- ♂ (169 bytes) () 07/18/2009 postreply 10:47:47

• 的确当时没细想。不过， -Commentate- ♂ (136 bytes) () 07/18/2009 postreply 15:20:43

• 解释一下我的想法 -雪山飞鱼- ♂ (479 bytes) () 07/18/2009 postreply 16:11:32

• 不是很明白 -Commentate- ♂ (259 bytes) () 07/18/2009 postreply 18:31:39