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 #1
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Mar 23, 2014
Mar 22, 2014
 #26
avatar+2354 
+11
Here are the new probability puzzles!
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Easier one:
A special machine contains 100 red, 100 green and 100 blue marbles.
The machine performs the following four operations.

First, the machine randomly picks 50 marbles from the entire batch.

Secondly the machine divides the marbles into one group of 20 and one group of 30

Furthermore, the machine picks and shuffles 5 marbles of the group of 20 and 10 marbles of the group of 30.

Finally, the machine randomly chooses one of the final 15 marbles it picked and shows it to you.

Assuming you cannot see anything which happens inside the machine.

What are the odds the machine will show you a red marble?

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Hard one :

Steve has two routes (A and B) to travel to his girlfriend which he is indifferent about (see my amazing illustrational skills )

knipsel11.png

Steve has decided to play a game which makes him decide which route to pick.
He always waits where the road splits between route A and B until he either sees a train going from A to B or from B to A.
If the first train Steve sees goes from A to B he always takes route A and if the first train Steve sees is a train going from B to A he always takes route B.
There are equally as many trains going from A to B as there are going from B to A.
Nevertheless Steve has noticed that for every five times he visits his girlfriend he takes route A four times and route B only once.

How can this be?

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Reinout-g

edit: I updated a flaw in the illustration, 'work' was meant to be 'girlfriend'
Mar 22, 2014
 #5
avatar+2354 
0
radamus:
Phida:

How do you Solve this?
2(x+3) - 2x^2(x+3) = 0
In my answer sheet they rewrite it to (x+3) * (2-2x^2) = 0
Im unsure what happens to the other (x+3)
Thank you in advance !



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Simpler to do it differently than your answer sheet

Divide both sides of the equation by 2 and you get (don't forget 0 divided by anything is 0)
(x+3) - x^2(x+3) = 0

Divide by (x+3) and you get
1 - x^2 = 0

Divide by -1 and you get
-1 + x^2 = 0

Add 1 to both sides of the equation and get
0 + x^2 = 1

x^2 = 1
x = 1



Hey radamus,

Thanks for your help on the answer,
However, I do have two remarks on your answer.

Primarily, x 2 = 1 has two answers, both x = -1 and x = 1 since (-1) 2 = 1 is also correct

Secondly, you can't simply divide by (x+3) since for x = -3, you would be dividing by 0.
In your answer this means that the answer x = -3 was left out.

If you fill in x = -3 in the equation, you'll find that it is also correct.

Off-topic

To show you something fun which you can do by dividing by 0, here is a fallacious proof that 1 = 2

Step 1 Let a=b.
Step 2: Then a2 = ab,
Step 3: a2 + a2 = a2 + ab,
Step 4: 2a2 = a2 + ab,
Step 5: 2a2 - 2ab = a2 + ab - 2ab,
Step 6: and 2a2 - 2ab = a2 - ab
Step 7: This can be written as 2 ( a2 - ab) = a2 - ab,
Step 8: and cancelling the ( a2 - ab) from both sides gives 1=2.

Now in step 8, the mathematician divided by a2 - ab, but since a=b, a2 - ab = a2 - a2 = 0

That's why you should never divide by something which could be 0.

Reinout
Mar 22, 2014
 #1
avatar+118725 
0
bump
Mar 22, 2014

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