Brain Teasers

[Pauldohert]

This is the crux of it for me. The showing of the third door allows the first door to conform to the first criterion you described.

There is now an equal chance that door 1 and 2 will confirm to the second criterion unless the first door is somewhat fatigued from the first event.

The first door doesn't have to conform to the first criterion on both occasions.

Are you saying its 50/50?

 

[dan-cat]

Thats correct.

The problem is, is that both door 1 and 2 have conformed to the same criterion but you want to apply the consequences of this conformation differently to each door.

 

[chergh]

A local entrepeneur bought 100 pounds of strawberries for $2.00 per pound and expected to double his investment by selling the strawberries for $4.00 per pound on a convenient street corner. The seller only managed to sell 50 pounds of strawberries the first day and he sold the remainder on the second day. The fresh strawberries had a content of 99% water, but because of the hot weather, the strawberries dehydrated and contained only 98% water on the second day. How much profit did the seller make?

Cost of Strawberries = $200

Day 1 Sales: 50 * $4 = $200

So 50 pounds of strawberries with 1% strawberry content =

1% * 50 Pounds = 0.5 pound strawberry content


0.5 pounds/2% = New Weight/100%

New Weight = (0.5 * 100)/2

New Weight = 25 Pounds

25 pounds * $4 = $100

Total Revenue = $300

Total Expenditure = $200

Profite = $100

 

[dan-cat]

Are you saying its 50/50?

You can't have it both ways.

If door 1 remains 1 in 3, then so does door 2.

There is no benefit in switching because both doors still contain the same probability.

 

[Pauldohert]

Sorry, your answer is not correct.

Maybe Ishould have done sales and added it up (definately adding day 1 and 2 would be good) to get

50 * 4 + 25* 4 = 300 = 200 profit?

Oh no - thats not right either - I worked out the expenditure wrong too.

 

[chergh]

I dunno -

Since Infinity + 1 is a valid number - So infinity hotel gets one bigger and the guest gets to stay?

No but your thinking is in the right place.

 

[ChipperT]

No but your thinking is in the right place.

If the number of rooms is infinite then there will always be room for one more since you cannot fill up an infinite (non-ending) number of rooms.

Infinite number of guests + 1 = infinite number of guests

 

[Access_guy49]

Originally Posted by ChipperT
A local entrepeneur bought 100 pounds of strawberries for $2.00 per pound and expected to double his investment by selling the strawberries for $4.00 per pound on a convenient street corner. The seller only managed to sell 50 pounds of strawberries the first day and he sold the remainder on the second day. The fresh strawberries had a content of 99% water, but because of the hot weather, the strawberries dehydrated and contained only 98% water on the second day. How much profit did the seller make?

Farm purcahsed 100 pounds at $2. = $200 expense.
First day, sold 50 pounds fresh strawberries at $4.00 = $200 (expenses = 0 now)

Second day..
Loss of 1%.
50 pounds x 0.01 = 0.5 pounds.
50 - 0.5 = 49.5 pounds.
49.5 pounds x $4 = 198 (profit)

 

[Pauldohert]

You can't have it both ways.

If door 1 remains 1 in 3, then so does door 2.

There is no benefit in switching because both doors still contain the same probability.

The probability must add up to 100/100.

It cant be explained better than already tried.

All I can say is try it on a friend and it becomes obvious its not 50/50

then look back at the explanations to see why.

Do it with 5 doors or something.

 

[ChipperT]

Farm purcahsed 100 pounds at $2. = $200 expense.
First day, sold 50 pounds fresh strawberries at $4.00 = $200 (expenses = 0 now)

Second day..
Loss of 1%.
50 pounds x 0.01 = 0.5 pounds.
50 - 0.5 = 49.5 pounds.
49.5 pounds x $4 = 198 (profit)

No, wrong answer.

 

[ChipperT]

Chergh: You are correct.

 

[Pauldohert]

My 3rd and final guess - is Chergh is correct.

You mean Chergh.

 

[Kryst51]

No, wrong answer.

I think if there was a 1% loss in weight then there would be a 1% loss in profit, so if the first day he made $100 then the second day he would make the $100 - 1% of $100, so $100-$1 = $199

 

[Pauldohert]

No but your thinking is in the right place.

I would only paraphrase my original answer if I tried again.

Time for a white answer!

 

[ChipperT]

I think if there was a 1% loss in weight then there would be a 1% loss in profit, so if the first day he made $100 then the second day he would make the $100 - 1% of $100, so $100-$1 = $199

Sorry, no prize behind door #2 for you... yet...

 

[Kryst51]

Sorry, no prize behind door #2 for you... yet...

Ha! I went up and read Cherghs answer, which you said was correct. So I know I was wrong.... But you can't blame a girl for trying.

 

[dan-cat]

The probability must add up to 100/100.

Here is where I don't follow.

A door can always be excluded - you know this before you start. So before you start your odds are 1/3 - and since you know nothing more about your original pick now - its odds of being coorect are still 1/3- and the remaining odds 2/3 must be on the other door.

You know nothing more about either door but you apply different rules to each door. Why can the odds on door2 change but not for door1 when they both conform to the rule of knowing nothing more about them?

How does guessing at door1 force door2 to become immune to your rule?

 

[Pauldohert]

Sorry, your answer is not correct.

My mistake was day 2 he doesn't make a profit! Isn't it? Arggh!

Keep them coming.

 

[Pauldohert]

Here is where I don't follow.



You know nothing more about either door but you apply different rules to each door. Why can the odds on door2 change but not for door1 when they both conform to the rule of knowing nothing more about them?

How does guessing at door1 force door2 to become immune to your rule?

As I said - its been explained as well as seemingly able to - so try it for real - with money.

But

You do know more about door 2 after the reveal , cos door 2 was part of the group that was 2/3 chance of being right. But you know the rest of that set ie door 3 is definatley wrong. So the 2/3 chance is all concentrated in door 2.

The choice is really were you likely to be right first pick or not.
We are all agreed I think, that the chances of that was only 1/3 - still is. So switch.

 

[Access_guy49]

Chergh: You are correct.

How is it that a 1% reduction in water is a 50% reduction in weight.... this answer can't be correct based on the info.

If the first day, the water content was 99% and that equates to 50 pounds.
Strawberry weight is 0.5 and water weight is 49.5

Looking at Just the water, we loose 1% of our water due to evap.
1% being 0.495 pounds of water.
Day two would have a water weight of 49.5 - 0.495 = 49.005

The weight of the strawberries stays the same at 0.5 which means we add them
49.005 + .5 = 49.505

Loss of 50% weight doesn't make any sense.