The Monty Hall Problem

You are on a TV show. You are given a choice of 3 doors. Behind one door is a car; behind the others, goats. You are to pick a door, winning whatever is behind it. So you pick one, say door 1. Since there are 2 goats behind 3 doors, whatever you choose, there is at least one goat left behind the 2 other doors. The host, Monty Hall, who knows what's behind them, opens one of these 2 other doors, say door 3, to reveal a goat. He then asks you, "Do you want to stick to your choice, or do you want to switch to door 2?" The question really is to ask, "Does switching increase your chance of winning the car?"
When you pick door 1, the chance of winning the car is 1/3 (i.e. the chance of having the car behind door 1 is 1/3 since there is 1 car in 3 possible doors). And then Monty eliminates door 3 for you by revealing a goat behind door 3. Intuitively, you think you then get a better chance of winning the car as the chance of having the car in door 1 is now 1/2 (since there is 1 car in only 2 possible doors) and likewise in door 2 is also 1/2. So you think it makes no difference whether to switch or not. So you choose to stick with door 1. Right? WRONG!

Let's go back and examine the probabilities in more details.

When you pick door 1, your chance of having the car behind door 1 is 1/3. There's no question about it. Let's now group doors 2 and 3 together. Your chance of having the car NOT behind door 1 (i.e. behind either door 2 or 3) is 2/3 since the total probability must equal to 1. By eliminating door 3 from the scene (by Monty), your chance of having the car behind door 1 is NOT increased from 1/3 to 1/2 as intuitively thought. Your chance of having the car in door 1 is still 1/3 as when you make your choice, you choose 1 out of 3 possibilities (doors 1, 2 and 3). As the saying goes, the dice has been cast. The probability will not, and cannot be altered. Only IF you are free to choose at this point, you are then to choose 1 out of 2 possibilities (doors 1 and 2), and the chance of having the car behind door 1 is indeed 1/2. So by eliminating door 3 from the scene, the effect is ONLY simply changing our group consisting of doors 2 and 3 to a group consisting of door 2 only. Hence your chance of having the car NOT behind door 1 (now behind door 2 only) is still 2/3. In other words, AT THIS POINT, the chance of having the car behind door 2 is 2/3, not 1/2 as intuitively thought. So after Monty eliminates door 3 for you by revealing a goat behind door 3, the chance of having a car in door 1 is 1/3, and in door 2 is 2/3.
Hence, YES, you WILL increase your chance of winning by switching. IN THEORY, YOU SHOULD ALWAYS SWITCH.

Behind the Shadow of The Father

It was a very hot summer day. The whole world seemed to be burning. Inside an air-conditioned clinic, a doctor was still feeling the heat outside. He raised his head and looked through the window. He saw hawkers busy selling their stuff on the street, hustling and bustling under the red hot sun. Before long, he heard very noisy sounds. Several people carried a big fellow into the clinic. The man had already fainted, with sweat all over his body. A little young girl was following and crying.
After the doctor's examination, the man was found to have gotten a sun-stroke. He was then given some water and an injection, and gradually regained his consciousness. Seeing her father recovered, the little girl was relieved despite still sobbing. She took out her purse, put all the money she got on the table and wanted to pay the doctor for the medical treatment. The doctor said, "Forget it. You may take this as a little help from me." The little girl thanked the doctor but continued crying. Trying to cheer up the little girl, the doctor said, "Don't cry, sweetheart. I know you are a strong girl. You were out in the sun all day and you are still okay. Look at your dad, he isn't as strong as you are." The girl cried even more loudly. She said, " No! It's not true! Dad asked me to sit behind his shadow all the time. It was him who stood up there, blocking the sun away from me all day. That's why I'm okay and he's not!"

A father's love is usually straightforward, pragmatic and yet mostly unspoken. Like a mother's love, it is also always dedicated, unconditional and unreserved, and is readily available when you need it. While we usually tend to praise mother's love more, do take a moment to appreciate the love from the father.

月亮代表我的心

This is a translation of the song 'The Moon Reflects All In My Heart' (月亮代表我的心) by Teresa Teng (鄧麗君) : 1953-1995. It's a very beautiful song sung by a very beautiful voice. Hope you enjoy!

You asked me how intimate my love is, how much I love you,
My passion's real, my love's real too.
The moon reflects all in my heart!

You asked me how intimate my love is, how much I love you,
My passion ne'er fades, my love ne'er dies.
The moon reflects all in my heart!

It was just a soft and tender kiss from you,
but it'd already touched the bottom of my heart.
It was such an unforgettable affair with you,
and it did make me miss you every moment till this time.

You asked me how intimate my love is, how much I love you,
You just go have a think, you just go have a look.
The moon reflects all in my heart!

你問我愛你有多深　我愛你有幾分
我的情也真　我的愛也真
月亮代表我的心

你問我愛你有多深　我愛你有幾分
我的情不移　我的愛不變
月亮代表我的心

輕輕的一個吻　已經打動我的心
深深的一段情　教我思念到如今

你問我愛你有多深　我愛你有幾分
你去想一想　你去看一看
月亮代表我的心

(extract from http://www.youtube.com/watch?v=51xS4yXbryc).

Wife : Girlfriend = TV : Mobile

Wife is like TV.
Girlfriend is like MOBILE (Phone).

At home watch TV.
Go out bring MOBILE.

No money, sell TV.
Got money change MOBILE.

Sometimes enjoy TV.
But most of the time you play with MOBILE.

TV is free for life.
For MOBILE if you don't pay, the services will be terminated.

TV is big, bulky and most of the time old.
MOBILE is cute, slim, curvy and portable at any time.

Operational cost for TV is acceptable.
Cost for MOBILE is high and often demanding.

TV has remote.
MOBILE doesn't.

With TV you MUST listen.
MOBILE is for two-way communications (you talk and listen).

TV do not have virus.
MOBILE? Definitely yes!

Wife vs Computer

I heard this from my friend (an IT guy) :

Wife can be mapped to a computer:
1. You face it everyday, and yet you still don't understand its complicated logic and difficult procedures.
2. It runs simple programs, which take you days to debug their errors.
3. It performs fast and accurate computations. It can compute how much salary to the dollar you still get left, and how much money you need in each single day in matter of nanoseconds.
4. It has superb memory and storage. Your every minor mistakes are stored securely and permanently on file, and can be recalled momentarily as and when required.
5. It organizes everything for you systematically: which restaurant to go, what tie to wear and when to see the in-law.
6. It is expensive to purchase. It is even more expensive to purchase the associated software and peripherals.
7. One minor careless mistake will cause it to crash. You need to spend a fortune and weeks to repair and restore for recovery.
8. It hangs up from time to time for no reasons, but will resume its operations automatically without your knowing.
9. It is your most precious toy and tool ever in life that you love and hate.

I Wish .........................

One day, a pair of young lovers went for a sightseeing trip on a bus, the destination of which was a famous tourist attraction. Before the bus entered the hills area, it passed by a small beautiful beach. The scenaries of the beach fully fascinated the pair. The man said to his girl friend, "Before going to the hills, why don't we go to the beach for a walk?" The girl said, " Good idea. I'd love to." So the man pressed the bell to signal to disembark. Afterwards, the bus continued to drive on slowly. The pair walked leisurely in the direction to the beach. But very shortly, they heard a sudden big "BOOM". A hugh boulder rolled down from the hill and struck right on the bus. Very unfortunately, no passengers on the bus survived.
Shocked at the scene, the man said to his girl friend very sadly, "I wish we were still on the bus." The girl was speechless with tears all over her face. She held her boyfriend's hand tight and nodded her head hard in agreement.

Under such situation, people might think about themselves first. They would feel happy and lucky to have gotten off the bus; otherwise they would be killed too. But the pair concerned more about the others and looked at the matter from a broader perspective. They thought that if they were still on the bus, the bus wouldn't have stopped but continued. When the boulder fell down, it wouldn't have hit the bus and the tragedy wouldn't have happened at all! They felt very sorry to have disembarked and not to have stayed with the other passengers!

Endless Love

Joe lived in a small town. He has been looking for job for some time. One afternoon, he went out for the job hunt as usual. On his way driving back home, Joe saw an old lady standing helplessly beside her car which had just broken down. Joe stopped his car and said to the old lady, "Madam, it's cold out here. Take your seat in the car and let me fix it for you." After Joe fixed the car, the old lady wanted to give some money to Joe as appreciation, but Joe declined. He said, "If you really want to show appreciation to me, can I ask you that next time you saw others needing help, you lend your hand too." The old lady nodded and happily drove her car away.
Later, the old lady went to a coffee shop. A waitress came up to serve her, and saw her hair was all wet with sweat. The waitress gave her a towel. The old lady noticed that the waitress was very tired from her look, and further noticed that the waitress was pregnant. Despite having to work the whole day for making a living, the waitress still served the old lady eagerly with warm smiles. After the old lady finished with her meal, she paid the bill and, in addition, she took out a $100 from her pocket, put on the tray and gave to the waitress before leaving the coffee shop. On the tray, there was written a small note, "Today I have been helped by a kind gentleman. I wish I can offer in turn some help to you. Please extend this piece of love by lending your hand to others needing help too." The waitress read the note and was deeply moved.
That evening, the waitress went home after work. Her husband was there. She took out the $100, told him what happened and gave it to him. She then sat beside him and gave him a kiss, "Don't worry. Things will soon be alright, Joe."

Joe was the kind man who helped the old lady to fix her car in the afternoon!

The Seven Bridges of Konigsberg

Konigsberg was a small town in East Prussia (now Russia), divided by a river into several parts which were connected by seven bridges as shown in the diagram. The citizens of Konigsberg crossed these bridges for leisure walks on Sundays. One day, they wondered, "Can we take a walk in Konigsberg in such a way that we cross each of the seven bridges once and only once?"

At first sight, we seem to be faced with a tedious and daunting task of tracing out all the possible routes with the seven bridges, and showing whether there is a particular route that works. To address such problem more systematically may require techniques of topology and the like. But when Leonhard Euler (1707-1783) looked at the problem, he immediately claimed that it was NOT possible to have such a walk. Despite Euler (pronounced as "oi-ler") was a great mathematician, he was able to prove his claim by a simple and clever way which can be understood by almost anyone. Euler's strategy to tackle the problem was by method of proof by contradiction. Now let's see how the genius was at work:

First note that Konigsberg is divided into FOUR regions, A, B, C and D interconnected by the seven bridges as shown in the diagram. Next assume that it IS possible to have a walk in the town by crossing each of the seven bridges once and only once. The walk may start in any one of the 4 regions, A, B, C or D, and end in any one of them (which may or may not be the starting region). In any case, we must have at least TWO regions which are neither the starting region nor the ending region.
Now consider any one of these regions. Since it is not the starting region nor the ending region, if we go into this region to visit, we must go out from it accordingly. To visit this region once, we have to go into the region through one bridge and out through another since we cannot cross the same bridge more than once. So we have to have 2 bridges connected to this region in order to visit it once. If we visit this region a couple of times, we have to have an even number of bridges so that we don't cross the same bridge more than once. But looking at the diagram, NO region in this town has such a property (i.e. connected with an even number of bridges: the island C has 5 bridges while the other regions A, B and D all have 3 bridges each), let alone there are at least 2 such regions. Hence, our original assumption that it IS possible to have such a walk leads to some contradiction to the given facts, and thus it cannot possibly be true. In other words, we cannot have a walk in Konigsberg by crossing each of the seven bridges once and only once.

Q. E. D.

空籠

最近記起一個關於亞嘛的故事.

有一天，亞嘛, 大哥, 大嫂，威伯伯，姑媽和我們幾人飲早茶. 吃過一輪點心後, 亞嘛想將吃完了空的點心籠, 放到枱邊, 以便侍應容易收拾. 亞嘛看到坐在對面的大嫂, 正在津津有味地吃着蝦餃. 亞嘛指着她說, "亞嫂, 你嗰邊有冇籠空（隆胸)?" 大嫂嚇了一跳. 蝦餃差點兒哽在喉嚨裡. 她連忙向亞嘛灑手, 急促地說, "細聲, 細聲點 ! 我冇, 我冇呀 !" 亞嘛看了她一眼, 更加提高聲響地說, "乜話? 我明明見到你有籠空. 仲話冇?"
全場一時為之嘩然 ! 大嫂差一點要躲到枱底下去了.

甚麼？

有一天, 媽媽,志瀚和我到一間餐館吃飯. 點過菜後, 我發覺枱面只得兩對筷子, 於是便揮手向一位侍應小姐示意, 打算向她再取多一雙. 那小姐慢慢地走過來問我, "先生, 你想要些甚麼?" 我説, "我想要筷子." 那小姐愣了一下, 走到柜面找了一會, 然後拿着一張空白的 A4 紙回來給我.

老天！我明白了那位小姐為何會猶豫. 原來她以為我説, "我想要塊紙."!