CP's math question

[M.]

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？

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]

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.

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  :

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......

[wongyan]

I will swap.....as the $100  is free......

The utility is not linear go wor. 

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

[kido]

The utility is not linear go wor. 

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

Not quite understand, explain the decision for both case please.....

[chin]

OK this is not exactly from CP, but he weighted in in the answer. The question is very simple, what is the answer to the following
6÷ 2(1+2)

I am so surprised that half the people answered 9, while almost half answered 1, and a small percentage came up with other number. I was told that this question have been circulated on the internet, and the general trend is half half 9 & 1.

After explaining why the answer should be 9, and the misleading part of the question, many who answered 1 still do not believe the answer!

I though any one went through high school math should know that division and multiplication are essentially the same - to divide by a number X is to multiply it by 1/X. So these two operation is the same in priority.

I am using my kid's programmable calculator to show the same.

[kido]

I understand both side 's arguement, one side says it's similAr to 1-2+3, it should be seen as -1+3=2, using other side's argument would evaluate 1-5=-4, also the priority of multiplication and divisions the same, hence the answer should be 3*3=9.

The other side view the formula as 6 / 2x and x is 3. And thus I think this is a case of ambiguity. I personally would like to view it as later case 

[hangchoi]

I understand both side 's arguement, one side says it's similAr to 1-2+3, it should be seen as -1+3=2, using other side's argument would evaluate 1-5=-4, also the priority of multiplication and divisions the same, hence the answer should be 3*3=9.

The other side view the formula as 6 / 2x and x is 3. And thus I think this is a case of ambiguity. I personally would like to view it as later case 

I concur.....

[q]

I started by answering 1.  The reason being that I read the divide as setting up numerator 6 and denominator 2(1 + 2), but of course its the wrong answer.