I have to talk to my class for about 10 minutes about why something works mathematically. I'm struggling with this because I have no ideas on what to do.
ok, a good math problem that most people will get wrong is one i read in a book called "the curious incident of the dog in the night time"
the question is, if you are on a game show and there are three doors in front of you, there is a goat behind two of them (a bad thing) and a car behind one of them (a good thing – change them to a pile of cash or a dung heap or wateva if u want).
You choose one, you have no way of knowing which is which.
Then the game show host opens a DIFERENT door from the one you chose and shows you it is a goat.
You have the option to switch to the other door and keep what is behind that, or stick withyour original choice.
Now, here's the math part, most people think that you now have a 50/50 chance, THEY ARE WRONG.
In fact, you have a 2/3 chance of getting a car if you switch, and a 1/3 chance of getting a car if you stick.
This is because the chance of getting a car was allready 1/3.
When the host took away a goat, that didn't change what was behind YOUR door.
here is a kinda graph to explain – we will say the car is behins door 3.
you first pick door 1 – a goat – you switch – CAR 
– you stick – goat 
you first pick door 2 – a goat – you switch – CAR
– you stick – goat
you first pick door 3 – a car – you switch – goat
– you stick -CAR
as you can see, 2 times out of 3, when you switch, you get a car.
If people disagree with you, you can say if there were a million lottery tickets and you picked 1, then the host took away 999998 of them, leaving only the 1 you picked, and one other.
if one of these is right, it is more likely that it is the one the host picked, because you had a chance of 1 in a million, and the host knew which one was right.
if you are in an advanced math class, and want the equation, you can find it in the back of the book i mentioned, they should have it in your school/local library, but it is quite complicated, and unless you are expected to do really complicated stuff, just stick with explaining the graph.
if you have any questions, contact me, and i'll put modifications in my answer here!
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ok, a good math problem that most people will get wrong is one i read in a book called "the curious incident of the dog in the night time"
the question is, if you are on a game show and there are three doors in front of you, there is a goat behind two of them (a bad thing) and a car behind one of them (a good thing – change them to a pile of cash or a dung heap or wateva if u want).
You choose one, you have no way of knowing which is which.
Then the game show host opens a DIFERENT door from the one you chose and shows you it is a goat.
You have the option to switch to the other door and keep what is behind that, or stick withyour original choice.
Now, here's the math part, most people think that you now have a 50/50 chance, THEY ARE WRONG.
In fact, you have a 2/3 chance of getting a car if you switch, and a 1/3 chance of getting a car if you stick.
This is because the chance of getting a car was allready 1/3.
When the host took away a goat, that didn't change what was behind YOUR door.
here is a kinda graph to explain – we will say the car is behins door 3.
you first pick door 1 – a goat – you switch – CAR
– you stick – goat
you first pick door 2 – a goat – you switch – CAR
– you stick – goat
you first pick door 3 – a car – you switch – goat
– you stick -CAR
as you can see, 2 times out of 3, when you switch, you get a car.
If people disagree with you, you can say if there were a million lottery tickets and you picked 1, then the host took away 999998 of them, leaving only the 1 you picked, and one other.
if one of these is right, it is more likely that it is the one the host picked, because you had a chance of 1 in a million, and the host knew which one was right.
if you are in an advanced math class, and want the equation, you can find it in the back of the book i mentioned, they should have it in your school/local library, but it is quite complicated, and unless you are expected to do really complicated stuff, just stick with explaining the graph.
if you have any questions, contact me, and i'll put modifications in my answer here!
References :
novel "the curious incedent of the dog in the night time"