I have three envelopes, into one of them I put a $20 note. I lay the envelopes out on a table in front of me and allow you to pick one envelope. You hold but do not open this envelope. I then take one of the envelopes from the table, demonstrate to you that it was empty, screw it up and throw it away. The question is would you rather stick with the envelope you have selected or exchange it for the one on the table. Why? What would be the expected value to you of the exchange? -Riddles

I have three envelopes, into one of them I put a $20 note. I lay the envelopes out on a table in front of me and allow you to pick one envelope. You hold but do not open this envelope. I then take one of the envelopes from the table, demonstrate to you that it was empty, screw it up and throw it away. The question is would you rather stick with the envelope you have selected or exchange it for the one on the table. Why? What would be the expected value to you of the exchange? -Riddles
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1 Answer

Answer :

The answer might seem a little counter intuitive at first but we'll see... The short answer is that it is in your advantage to exchange. But why? Well initially there was a 1/3 chance that you were holding the envelope with the note in it and a 2/3 chance that the note was on the table. This is still the case after one of the envelopes on the table has been removed, there is still a 1/3 chance that you have the note and a 2/3 chance of it being on the table. If this is confusing then it may help to think that the questioner knows which envelope the $20 note is in, though in practice it doesn't actually matter. The questioner would always be able to demonstrate that the note was not in one of the envelopes on the table regardless of where the note was, so the fact that he was able to do this changes nothing. Consider a different example.... Say there are a 1000 envelopes on the table, 1 with a note inside. You pick 1 envelope, the chance that this has the note in it is clearly 1/1000, where as the chance that it is still on the table is 999/1000. Odds are its on the table. Now the questioner could, assuming he can remember where the note is demonstrate to you that the note is not in 998 of the envelopes on the table. In this case nothing would have happened to change the fact that there is only a 1/1000 chance of you having the note. That is why you exchange. What is the value of the exchange? Simply before the exchange you have 1/3 of $20 and afterwards you will have 2/3 of $20, ie the advantage to you is about $6.66
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Related questions

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Description : Two women sit staring and glaring at each other across a small table. Although the two women don't appear to be friendly toward each other, they do eventually hold each other's hands. A man approaches, puts ... is the word the man shouts to the women, and what in the world is going on here? -Riddles

Last Answer : The word the man shouts to the women is, 'Go!' This is the way most women's arm wrestling competitions start, and hopefully the wrist straps, to keep their hands from slipping apart, won't have to be used.

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Last Answer : Answer: A Let the sums of money received by A, B and C be x, y and z respectively. Then x - 10 : y - 20 : z -15 is 11a : 18a : 24a When $10, $20 and $15 are removed, we are removing a total of $45 from ... or a= 20 We know that z - 15 = 24a = (24 * 20) = 480 Therefore, z = 480 + 15 = $495

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Description : There is a clothing store in Bartlesville. The owner has devised his own method of pricing items. A vest costs $20, socks cost $25, a tie costs $15 and a blouse costs $30. Using the method, how much would a pair of underwear cost? -Riddles

Last Answer : $45. The pricing method consists of charging $5 for each letter required to spell the item.

A new clothing store has a unique method of pricing items. A vest costs $20, a tie costs $15, a blouse costs $30, and underwear costs $45. How much would pants cost? -Riddles

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Last Answer : $25. The pricing method charges $5 for each letter needed to spell the item.

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Description : A man strolls into a hospital emergency room where there is a long line up to the reception desk. He walks right to the front and clamly asks to see the consultant in charge. No one gets angry and ... The consultant has never met this man, yet she hurries away from the ward to see him.Why? -Riddles

Last Answer : The man is a florist delievering a bouquet of flowers for the consultant.

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Last Answer : Well Duh! The outside of the Cat of course!

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Description : Dynamite is a tool that can be used to cut down trees. To cut a tree 18 inches in diameter requires five sticks of dynamite: one on the north, south, east and west sides of the tree, and the ... you instruct the diver to put the fifth stick of dynamite if you wanted the tree to fall north? -Riddles

Last Answer : It doesn't matter where the fifth stick is placed, since the tree won't fall in any direction. Being wood, it will float and rise to the surface.

In the back yard, there is a hollow stump, that contains six ears of corn. If a healthy squirrel carries out only three ears each day, how many days will it take to empty the stump? -Riddles

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Last Answer : Six. Each day the squirrel will carry out the two ears on his head plus one ear of corn.

What do you throw out when you want to use it but take in when you don't want to use it? -Riddles

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Last Answer : An anchor.

You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weight the same or that the dish that falls lower has heavier contents than the other. The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of a different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more. Note that the unusual marble may be heavier or lighter than the others. You are asked to both identify it and determine whether it is heavy or light -Riddles

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Why did the girl throw a stick of butter out of her window?

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Last Answer : She wanted to see a butterfly.

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Old Mr. Tilly was found dead in his study by Mr. Foster. Mr. Foster recounted his dismal discovery to the police. 'I was walking by Mr. Tilly`s house when I thought I would just pop in for a visit. I noticed his study light was on and I decided to peek in from the outside to see if he was in there. There was frost on the window, so I had to wipe it away to see inside. That is when I saw his body. So I kicked in the front door to confirm my suspicions of foul play. I called the police immediately afterward.' The officer immediately arrested Mr. Foster for the murder of Mr. Tilly. How did he know Mr. Foster was lying? -Riddles

Description : Old Mr. Tilly was found dead in his study by Mr. Foster. Mr. Foster recounted his dismal discovery to the police. 'I was walking by Mr. Tilly`s house when I thought I would just pop in for a ... arrested Mr. Foster for the murder of Mr. Tilly. How did he know Mr. Foster was lying? -Riddles

Last Answer : Frost forms on the inside of the window, not the outside. So Mr. Foster could not have wiped it off to discover Mr. Tilly`s body.

You walk into your house the electricity is out you see three doors that you have never seen before. You go through the one with a lion that hasn't eaten for over six months. There are another three doors you go through the one with an empty room. There's a man that says how do you want to be murdered with the gun the knife or the electric chair that will kill you in an instant. How will you survive? -Riddles

Description : You walk into your house the electricity is out you see three doors that you have never seen before. You go through the one with a lion that hasn't eaten for over six months. There are another three ... the knife or the electric chair that will kill you in an instant. How will you survive? -Riddles

Last Answer : The electric chair because your electricity is out.

I come in a cone but I am not food;I will be skewed if you screw with my hue;I come by the millions but you can probably only name a few.What am I? -Riddles

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Last Answer : Colors.

A Lady was found dead in a park. There was a note on the lady, it read: 1491011. The suspects were Jason, Miranda, Sal, and Timmy. The police knew who it was right away. Who was it? -Riddles

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Last Answer : Jason. 1= January 4= April 9= September 10= October 11= November. The First Letter Of Each Month Ends Up Spelling Jason.