The worlds first riddle!

"I know the world is not fair" sometimes thee only fair in life is at a carnival.

Hi Try,,, i'm going to pretend you're my big brother,,, (don't mind me) :wink: .

[size=7]Three times

over 2 boys
back 1 boy
over 1sr soldier
back 1 boy

over 2 boys
back 1 boy
over 2nd soldier
back 1 boy

Over 2 boys
bacj 1 boy
over 3rd soldier
back 1 boy

68/87[/size]

Rap

I will pass on the river question. Shouldn't the answer just be 68/87=.78?

Rap:

Three times

over 2 boys
back 1 boy
over 1sr soldier
back 1 boy

over 2 boys
back 1 boy
over 2nd soldier
back 1 boy

Over 2 boys
back 1 boy
over 3rd soldier
back 1 boy

That will do nicely.



Probability

68/87



TTH:

Shouldn't the answer just be 68/87=.78?

You are right! When considering probability:

Divide the number of ways to choose a red marble (68) by the total number of marbles (87)
68 ÷ 87 = 0.781609
Round to the desired precision (e.g. 0.781609 rounded to hundredths is 0.78)

It is just that easy!




wtrryagotae


adgrae

That is just such a clever thing to say!

drainage

The only answer I can come up with is: tryagain wrote

TTH:

adgrae = drainage

wtrryagotae =
The only answer I can come up with is: tryagain wrote

You are a flipping genius!



TTH has an urn with four balls of different colors. Randomly you draw two at a time, then painting the first ball to match the second.

What is the expected number of drawings before all balls are the same color

2 as you didn't specify 'with replacement' and I didn't need to achieve the impossible of painting a first ball when "two are drawn at a time". Optional smiley face.

BALLS
[size=7]9[/size]

Good morning all.

After seeing the comment:

"2 as you didn't specify 'with replacement' and I didn't need to achieve the impossible of painting a first ball when "two are drawn at a time". Optional smiley face."

By none other than Slippy; I had prepared an - in your face, I win; sort of reply….

Unfortunately my exhilaration was short lived due entirely to Mark making an appearance at 3.45am!!!


Mark:

9



The answer is 9.

Call the four colors 1,2,3, and 4.

After the first turn you will have a configuration like 1,1,2,3. Call this configuration 1

From configuration 1 if you draw a 1 on the first ball you will end up with the same or similar configuration. The probability of this happening is 1/2.
From configuration 1 if you draw a 3 or 4 first and then a 1 you will have a configuration like 1,1,1,2. The probability of this happening is 1/3. Call this new pattern configuration 2.

From configuration 1 if you draw a 3 or 4 first and then draw the other non 1 you will have a configuration like 1,1,2,2. The probability of this is 1/6. Call this new pattern configuration 3.

From configuration 2 you will end up with the same pattern with probability 1/2, configuration 3 with probability 1/4, and ending the experiment with probability 1/4.

From configuration 3 you will end up with the same thing with probability 1/3, and with configuration 2 with probability 2/3.

From this information you can draw the following equations, where a is the expected number of turns from equation 1, b from equation 2, and c from equation 3:

a=(a+1)/2 + (b+1)/3 + (c+1)/6
b=(b+1)/2 + (1)/4 + (c+1)/4
c=(c+1)/3 + (2/3)*(b+1)

Finally simple matrix algebra will show a=8. Considering the first turn from the original condition to equation 1 the expected number of turns is indeed 9.




CUCHBICATKEENR


alfly

CUCHBICATKEENR =chicken incubater or incubator?
( Try, wanna borrow my dictionary? :wink: )


alfly =finally

I got what stormwatch got

Stormy:

CUCHBICATKEENR =chicken incubater or incubator?
( Try, wanna borrow my dictionary?

Both are good!

alfly =finally


TTH:

I got what stormwatch got


So did I!




There are two envelopes in front of you each with a non-zero number. You will receive an amount of money equal to the final envelope you choose. You are informed one has twice as much money as the other.

You are then allowed to select either envelope. After you select one and before opening it you are given the option to change your mind and switch to the other one.

You think to yourself that if your envelope has x dollars there is a 50% chance the other one has x/2 dollars and a 50% chance it has 2x dollars.

The expected return, you compute, is .5[.5x + 2x]=1.25x which seems like a favorable gamble.

Do you switch, and if so why


(Assume you are neither risk averse nor risk prone, in other words you will take any good gamble and avoid any bad one.)

Hi Try,,, how are you? You're moving? I would love to live in a castle in Europe. Altenburg Germany.

The kings in this video ~(Funker Vogt) are the king's on a deck of cards. Another relative of these men is

~'KinG JameS,.. a man in the stained glass at ~

~'Thee Episcopealean Church i sometimes frequent. They and i look like this mans relative's ~

http://www.wga.hu/art/m/master/zunk_ge/zunk_ge3/0altarpi.jpg

Look at what i found~

"This is a postcard from Spain, with supposedly each of the kings that the figures on a deck of cards were modeled after." ~



~ 'KinG JaMeS 'BeD@CH@eZ' YaWaY wrote this:

http://www.funnytheworld.com/JS-KINGS.jpg

"The Deck of Cards



During the North African Campaign, a bunch of soldier boys had been on a long hike. They arrived in a little town called Casino. The next morning being Sunday, several of the boys went to church. A sergeant commanded the boys in church.


After the Chaplain read the prayer, the text was taken up next. Those of the boys that had a prayer book took them out. One boy had only a deck of cards, and he spread them out. The sergeant saw the cards and said, "Soldier, put away those cards." After the service was over, the soldier was taken prisoner and brought before the Provost Marshal.


The Marshal said, "Sergeant, why have you brought this man here?"


"For playing cards in church, Sir," was the response.


The Marshal asked the soldier, "And what have you to say for yourself, son?"


"Much, Sir," replied the soldier.


The Marshal stated, "I hope so, for if not I will punish you more than any man was ever punished."


The soldier said, "Sir, I have been on the march for about six months. I have neither bible nor a prayer book, but I hope to satisfy you, sir, with the purity of my intentions." And with that, the boy started his story ...


"You see, sir, when I look at the Ace, it reminds me that there is but one God.
And the deuce reminds me that the bible is divided into two parts: the Old and the New Testaments.
When I see the trey, I think of the Father, the Son, and the Holy Spirit.
And when I see the four, I think of the four evangelists who preached the Gospel: there was Matthew, Mark, Luke and John.
And when I see the five, it reminds me of the five wise virgins who trimmed their lamps; there were ten of them: five were wise and were saved, five were foolish and were shut out.
When I see the six, it reminds me that in six days God made this heaven and earth.
And when I see the seven, it reminds me that on the seventh day, God rested from his great work.
And when I see the eight, I think of the eight righteous persons that God saved when he destroyed the earth: there was Noah, his wife, their sons and their wives.
And when I see the nine, I think of the lepers our saviour cleansed, and that nine of the ten didn't even thank him.
When I see the ten, I think of the ten commandments that God handed down to Moses on a tablet of stone.
When I see the King, it reminds me that there is but one King of Heaven, God Almighty.
And when I see the Queen, I think of the blessed Virgin Mary who is the Queen of Heaven.
And the Jack or Knave is the Devil.


When I count the number of spots in a deck of cards, I find 365, the number of days in a year.
There are 52 cards, the number of weeks in a year.
There are four suits, the number of weeks in a month.
There are twelve picture cards, the number of months in a year.
There are thirteen tricks, the number of weeks in a quarter.


So you see, Sir, my deck of cards serves me as a bible, an almanac and a prayer book."


The author and performer of "Deck of Cards" was
T. Texas Tyler.
He stated at the conclusion:
"And friends, this story is true.
I know ... I was that soldier."

I don't think it matters. The expectation of 1.25 exists only before you've chosen either envelope. Once you've picked one, it's a 50:50 chance you've got the greater.

So in my intuitive mind, the choice is yours. Are you a gambler? Do you take what you've got and run, or do you go for the greater?-----Additional conditions to consider
A) If the amount significant to you or your benefactor---if it isn't to either, pick the other envelope.
B) If the amount is considerable to you but not the benefactor its a draw
C) If the amount isn't considerable to you but is to the benefactor stick with your first pick
D) If the amount is considerable to both you and the benefactor again it's a draw.

Me I'm not a gambler--So in lieu with conditions B, C & D I'd stick with what I've got. If I was a gambler, I could make a case for making the opposite choice because of conditions A, B & D.

Rap

It's the switch for me.

ooo er.

Rap:

I don't think it matters. The expectation of 1.25 exists only before you've chosen either envelope. Once you've picked one, it's a 50:50 chance you've got the greater.

So in my intuitive mind, the choice is yours. Are you a gambler? Do you take what you've got and run, or do you go for the greater?-----Additional conditions to consider :

A) If the amount significant to you or your benefactor---if it isn't to either, pick the other envelope.

B) If the amount is considerable to you but not the benefactor its a draw.

C) If the amount isn't considerable to you but is to the benefactor stick with your first pick.


D) If the amount is considerable to both you and the benefactor again it's a draw.

Me I'm not a gambler--So in lieu with conditions B, C & D I'd stick with what I've got. If I was a gambler, I could make a case for making the opposite choice because of conditions A, B & D.


He is indeed correct, there is no advantage or disadvantage to switching.


This is a well known problem known as the "two envelope paradox." Sometimes it is asked where the player may open the first envelope before switching. The argument in favor of switching is that the other envelope has either half or twice as much, with 50% probability each. If there is $x is the first envelops then the expected value of the other envelope is ($2x+$0.5x)/2 = $1.25x.

However if this argument could be used to go back and forth infinitely if the first envelope is not opened. If you know the option will be granted in advance you could use it to save the trouble of switching and pick the other envelope in the first place, but then you could use it again to switch back again, infinitely.

Whether or not the first envelope is opened you cannot blindly say the other envelope might have twice as much. To make an extreme example if the total amount of money in the world is t and the first envelope has more than t/2 then it is impossible for the other envelope to have twice as much.

More practically if the person offering the money must have a finite amount to give. So we can't blindly say there is a 50% chance of doubling if the first envelope. For example if the person offering the envelopes has exactly $1,000,000 dollars the most he can offer is $500,000 and $1,000,000. So if the first envelope had $1,000,000 it would be impossible for the other envelope to have $2,000,000.

However let's take the case where a billionaire is hosting the game and the first envelope has less than $100. Any amount under $10,000 would mean nothing to the host. So bumping up against the maximum is apparently not an issue. A million players could use the expected value to switch, but would they be better off?

Indeed on average half would end with 200% of the first envelope and half 50%, for an average amount in the second envelope of 125% the first. However what is important is not the rate of increase but the amount of the increase. As a group switching will not have helped. This is the hard part to explain but when the switch was the right decision the player is doubling off of the small amount, and when it is wrong the player is halving from a larger amount.

Either way the decision to switch will result a win or loss of the amount in the smaller envelope. So the expected rate of increase is 25% but the expected amount of increase is $0. So although the expected rate of increase is 25% that does not mean the other envelope will have 25% more. The second envelope has a 100% chance of having 100% more if the first envelope is the smaller amount, and a 100% chance of having 50% less if the first envelope is the larger amount. So, once the first envelope is chosen the second envelope is no longer a random variable.

Using an increasing function, mapping values of x from 0 to infinity to 0 to 1, the player can improve his probability of ultimately choosing the correct envelope to above 50%. For example if the amount in the initial envelope is x and the player keeps his original envelope with probability x/(c+x), where c>0, then he will be more likely to not switch with the larger envelope.

Note that the function must be decided upon before the first envelope is chosen and a method must be available to choose a precise random number. To add my own comment you could also improve the probability of a successful switch above 50/50 by deciding in advance at what point you will switch.

For example I'll switch with $1000.005 (I add the 0.005 to avoid ties) or less in the first envelope. This will produce a 100% success rate if $1000.005 falls between the two envelope amounts, although only 50% otherwise.



Slippy on the other hand, wants' to get straight down to business. "It's the switch for me. Ooo er

Hi Jo,

"Hi Try,,, how are you? You're moving? I would love to live in a castle in Europe. Altenburg Germany"

So, you read the financial pages to know about the castle. Have no fear, I will not be living there, it is to be dismantled and shipped over block by block.

As for the cards; I will never play strip poker again!

Please girlies - someone get this......

I wanna see him eat his foot. Is that part of the fetish?

(I'm on meds. I don't need to Try!)