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But I was excited, too. Because I thought she might tell me a secret. And the secret might be about who killed Wellington. Or about Mr. Shears. And if she did that I might have more evidence against him, or be able to Exclude Him from My Investigations.
So because it was a Super Good Day I decided to walk into the park with Mrs. Alexander, even though it scared me.
When we were inside the park Mrs. Alexander stopped walking and said, “I am going to say something to you and you must promise not to tell your father that I told you this.”
I asked, “Why?”
And she said, “I shouldn’t have said what I said. And if I don’t explain, you’ll carry on wondering what I meant. And you might ask your father. And I don’t want you to do that because I don’t want you to upset him. So I’m going to explain why I said what I said. But before I do that you have to promise not to tell anyone I said this to you.”
I asked, “Why?”
And she said, “Christopher, please, just trust me.”
And I said, “I promise.” Because if Mrs. Alexander told me who killed Wellington, or she told me that Mr. Shears had really killed Mother, I could still go to the police and tell them because you are allowed to break a promise if someone has committed a crime and you know about it.
And Mrs. Alexander said, “Your mother, before she died, was very good friends with Mr. Shears.”
And I said, “I know.”
And she said, “No, Christopher. I’m not sure that you do. I mean that they were very good friends. Very, very good friends.”
I thought about this for a while and said, “Do you mean that they were doing sex?”
And Mrs. Alexander said, “Yes, Christopher. That is what I mean.”
Then she didn’t say anything for about 30 seconds. Then she said, “I’m sorry, Christopher. I really didn’t mean to say anything that was going to upset you. But I wanted to explain. Why I said what I said. You see, I thought you knew. That’s why your father thinks that Mr. Shears is an evil man. And that will be why he doesn’t want you going around talking to people about Mr. Shears. Because that will bring back bad memories.”
And I said, “Was that why Mr. Shears left Mrs. Shears, because he was doing sex with someone else when he was married to Mrs. Shears?”
And Mrs. Alexander said, “Yes, I expect so.”
Then she said, “I’m sorry, Christopher. I really am.”
And I said, “I think I should go now.”
And she said, “Are you OK, Christopher?”
And I said, “I’m scared of being in the park with you because you’re a stranger.”
And she said, “I’m not a stranger, Christopher, I’m a friend.”
And I said, “I’m going to go home now.”
And she said, “If you want to talk about this you can come and see me anytime you want. You only have to knock on my door.”
And I said, “OK.”
And she said, “Christopher?”
And I said, “What?”
And she said, “You won’t tell your father about this conversation, will you?”
And I said, “No. I promised.”
And she said, “You go on home. And remember what I said. Anytime.”
Then I went home.
101. Mr. Jeavons said that I liked maths because it was safe. He said I liked maths because it meant solving problems, and these problems were difficult and interesting but there was always a straightforward answer at the end. And what he meant was that maths wasn’t like life because in life there are no straightforward answers at the end. I know he meant this because this is what he said.
This is because Mr. Jeavons doesn’t understand numbers.
Here is a famous story called The Monty Hall Problem which I have included in this book because it illustrates what I mean.
There used to be a column called Ask Marilyn in a magazine called Parade in America. And this column was written by Marilyn vos Savant and in the magazine it said that she had the highest IQ in the world in the Gui
You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of the doors and there are goats behind the other two doors. He asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens one of the doors you didn’t pick to show a goat (because he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do?
Marilyn vos Savant said that you should always change and pick the final door because the chances are 2 in 3 that there will be a car behind that door.
But if you use your intuition you think that chance is 50-50 because you think there is an equal chance that the car is behind any door.
Lots of people wrote to the magazine to say that Marilyn vos Savant was wrong, even when she explained very carefully why she was right. Of the letters she got about the problem, 92% said that she was wrong and lots of these were from mathematicians and scientists. Here are some of the things that they said:
I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error.
There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame!
I am in shock that after being corrected by at least three mathematicians, you still do not see your mistake.
I am sure you will receive many letters from high school and college students. Perhaps you should keep a few addresses for help with future columns.
You are utterly incorrect… How many irate mathematicians are needed to get you to change your mind?
If all those Ph.D.’s were wrong, the country would be in very serious trouble.
But Marilyn vos Savant was right. And here are 2 ways you can show this.
Firstly you can do it by maths like this:
Let the doors be called X, Y and Z.
Let Cx be the event that the car is behind door X and so on.
Let Hx be the event that the host opens door X and so on.
Supposing that you choose door X, the possibility that you win a car if you then switch your choice is given by the following formula
P(Hz ^ Cy) + P(Hy ^ Cz)
= P(Cy)·P (Hz : Cy) + P(Cz)·P(Hy : Cz)
= (1/3 · 1) + (1/3 · 1) = 2/3
The second way you can work it out is by making a picture of all the possible outcomes like this: