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CP's math question

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M.:

--- Quote ---有個有趣問題！睇你會點揀！
如果有兩封利是，你可以揀一封，知道一封係另一封10倍錢(例如：如果一封係$100，另一封係$1000或者$10)。
而家比一封你，係未開既(假設係$100，咁另一封就係$1000或者$10)！
如果比機會你可以選擇另一封，你換唔換？點解？
--- End quote ---

The following are two Excel simulations:

I. the question is understood as pick one of the two Lai See, then the average value is the same.

II. the question is understood as you pick one first, then the other one is either only 10% or 1000% of the value.

kido:

--- Quote from: M. on 27 March 2011, 13:11:47 ---The following are two Excel simulations:

I. the question is understood as pick one of the two Lai See, then the average value is the same.

II. the question is understood as you pick one first, then the other one is either only 10% or 1000% of the value.

--- End quote ---

Interesting.... I & II should have same results. But obviously you got different.

Is that related to the problem posted previously?  

kido:
I just have another thought, using what I just learnt when I met Kelly last night  ;D ;D ;D ;D:

Assume you took $100 in first red pocket:

I. Do nothing:
  
Assume I do nothing : log (100) = 2


II. Swap.

There are two possible mutually exclusive possible outcome with 50%-50%:

A (50% happening) - it will be rised to $1000
B (50% happening) - will be reduced to $10

Calculate the following:

50% * log (1000) + 50% * log(10)
= 3/2 + 1/2
= 2

which are same... i.e. no different either change or not change.

hangchoi:
I will swap.....as the $100  is free...... :D

wongyan:

--- Quote from: hangchoi on 27 March 2011, 17:20:58 ---I will swap.....as the $100  is free...... :D



--- End quote ---
The utility is not linear go wor. 

e.g. 1,000,000  100,000 10,000 outcome will be different from 10m, 1million, 100k.

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