The Investor’s Gift Exchange Paradox

One fine day, an angel descends from heaven and picks you to offer a gift.

She displays two envelopes in front of her and tells you that the two envelopes both contain money.  However, she cannot tell you how much money is contained within the two sealed envelopes; all she can say is that one envelope contains 10,000 times the amount of money the other envelope contains.  To put that in another way, one envelope contains 1/10,000 of what the other envelope contains.  Which envelope you pick depends entirely upon your luck.

So you close your eyes and pick one of them.  You discover a $100 bill inside the envelope.  Now, the angel makes another offer to you.  “Would you like to exchange your envelope with the $100 bill for the other envelope which I’ve previously offered you but you’ve not chosen?”

Now, some of you might get incredulous.  You might ask, “Wouldn’t the two envelopes be the same?  If I had chosen the other envelope, wouldn’t I now be offered the current envelope?”

However, the answer is not that simple.  First of all, I need you to think like a truly rational, risk-taking investor.  Take a moment to ponder upon the question before you look at the answer.

The answer is that you should exchange the $100 bill for the other envelope.

You must remember that one envelope contains 10,000 times the amount of money that the other envelope contains.  So, the other envelope will contain either a meager 1 cent ($100/10000) or a whopping $1 million ($100X10000).  As an enterprising investor, surely you would risk a 50% chance of losing only nearly all of $100 or a 50% chance of winning the million-dollar jackpot.  In mathematical terms, the expected outcome of the exchange, E(x), is ($1,000,000+$0.01)/2 = $500,000.005.  This is a tremendously good offer by the benevolent angel.

Now, the question – do you see the contradictory paradox in the above passage?

Nice Inspirational Quotes

Heavy rains remind us of challenges in life. Never ask for a lighter rain. Just pray for a better umbrella. – That is attitude!

Life is not about finding the right person, but creating the right relationship, it’s not how we care in the beginning, but how much we care till the very end.

Some people always throw stones in your path. It depends on what you make with them. A Wall or a Bridge? – Remember you are the architect of your life.

Search for a beautiful heart, but don’t search for a beautiful face. Coz beautiful things are not always good, but good things are always beautiful.

It’s not important to hold all the good cards in life. But it’s important how well you play with the cards you hold.

Often when we lose all hope & think this is the end, God smiles from above and says, ‘relax dear it’s just a bend, not the end.’ – Have faith and have a successful life.

Be thankful in life….

You say you love rain, but you use an umbrella to walk under it. You say you love sun, but you seek shelter when it is shining. You say you love wind, but when it comes you close your windows. So that’s why I’m scared when you say you love me.

励志一文

在垃圾邮件里看到的一则短文:

积极的人在每一次忧患中都看到一个机会,而消极的人则在每个机会都看到某种忧患。
白日依山尽,黄河入海流。欲穷千里目,更上一层楼。
意识清楚的人很少畏惧任何东西。
以平心阅人情,以虚心求学问。