f***a
发帖数: 329 | 1 发信人: ogtree (好好努力), 信区: Quant
标 题: a probability question
发信站: BBS 未名空间站 (Wed Jul 21 21:48:46 2010, 美东)
Assume I have a 5 button keypad, with numbers 1-5 on it. Define E(X) =
expected number of keypresses to
open the door. Suppose my password is a two-digit number (no repeats), and
suppose a light goes on once
I've hit the correct first digit.
E(X)=? | s******y
发帖数: 352 | | a****t
发帖数: 7049 | 3 这是在问minimum expected number吧
最快解锁的办法是先穷举第一位数直到灯亮
然后穷举所有正确第一位打头的二位数密码
找到第一位数平均要3下，找到第二位平均2.5下，连带正确的第一位数就是5下，第一
位数头一次正确那次按数了两遍，所以答案是7。 | b*******r
发帖数: 152 | 4 i think it depends on if you are allowed to re-enter the first digit when
your first try fails. in other word, if the game rule says you have to enter
2 digits in a row, i don't think your solution is right. | o*********h
发帖数: 6 | 5 suppose I minimize the number of trying. To get the first digit correct (c1)
, there are 5 possibilities:
first try is the right number: c1
first number wrong, second try got correct: w11c1
tried 2 different wrong numbers, got third right: w11w12c1
tried 3 different wrong numbers, got forth right: w11w12w13w14c1
tried 4 different wrong numbers, got fifth right: w11w12w13w14c1
each has a probability of 1/5. Once we got the correct first digit, there
are 4 possible ways to get the second one is al | a****t
发帖数: 7049 | 6 我参考我见过的这种锁来理解。你按错了，等几秒就可以重新试了。
enter
【在 b*******r 的大作中提到】
: i think it depends on if you are allowed to re-enter the first digit when
: your first try fails. in other word, if the game rule says you have to enter
: 2 digits in a row, i don't think your solution is right.
| f***a
发帖数: 329 | |
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