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Topic created : 3 January 2012, 16:27

JustNash

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First and foremost, my best wishes to you all!

As some of you might not know what to do with the spare time due to the lack of updates recently, I thought it might be entertaining to try and start a chain of riddles. I'll go first with a simple one:

Imagine a New Year's gift: a set of 3 little boxes with 2 chocolates in each. 1 box contains 2 black chocolates, 1 box contains 2 white chocolates and the third has 1 black and 1 white chocolate. Now, without looking inside, open up a random box and take out a chocolate.
Question: if the chocolate is white, what are the odds that the other chocolate in that box is also white?
A. 1/3
B. 1/2
C. 2/3
D. ...mmmmm, chocolate...

I hope people will reply, preferably with just their choice. Keep the others guessing :-)

If you have a riddle, you can start a new thread and give it a number (eg Riddle 2).

Good luck!

Nash

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3 January 2012, 18:48

yuga_ninjie

Moderator

Yuga Ninjie Group of Company

hahaha... let me try...

Box 1: Probability of white is 0
Box 2: Probability of white is 1
Box 3: Probability of white is 1/2

Probability of choosing random box is 1/3

P = (RB)(B1)+(RB)(B2)+(RB)(B3)
P = (1/3)(0)+(1/3)(1)+(1/3)(1/2)
P = 1/2

Is this correct?

3 January 2012, 19:45

JustNash

Premium Brands

it might be correct, but it might not :-)

I'll give some more time to everybody to take a stab and confirm or disprove your response tomorrow :-)

Who agrees with yuga_ninjie? Who disagrees?

3 January 2012, 20:04

giekas

i.G33K

Veridian Dynamics

I hate probability problems Well

- never know how to interpret initial conditions correctly...

I'd say 'B' because this is not exactly Three Doors Paradox http://en.wikipedia.org/wiki/Monty_Hall_problem ...

P.S.
incidentally, aren't we solving your homework here ? Very we!

3 January 2012, 21:37

Geekrulez

Corponation

B ?
RANDOM. Its either white or black.

4 January 2012, 13:23

JustNash

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giekas
I hate probability problems - never know how to interpret initial conditions correctly...

I'd say 'B' because this is not exactly Three Doors Paradox http://en.wikipedia.org/wiki/Monty_Hall_problem ...

P.S.
incidentally, aren't we solving your homework here ?

Close, it is actually Bertrand's Box Paradox: http://en.wikipedia.org/wiki/Bertrand%27s_box_paradox ...
Although I didn't know that until I clicked your link to the Monty Hall problem :-)

And don't worry, you are not solving my homework (good one :-))

4 January 2012, 13:30

Last time edited : 4 January 2012, 13:31

JustNash

Premium Brands

I was also very much convinced that it was B: 50%. I even had an argument about it. But as it turns out, it is C: 2/3!

To me the easiest proof I've come across was: Imagine an audience of 300 recipients of the boxes. 150 of those will draw a white chocolate first, 150 will draw a black chocolate. 100 will have opened the box with 2 black chocolates, 100 will open the box with 2 white chocolates and 100 will open the box with one of each. Hence, there will be a total of 100 cases where the recipient will draw a second white chocolate out of his box.

100 divided by the amount of people drawing a white chocolate first (150) means that there is a 2/3 probability :-)

Thanks for participating!

Anybody with a new riddle?

5 January 2012, 00:50

Dutchsmurf

Smurf International

Let me guess, you are Dutch (actually, I know you are) and have been watching tv over the holiday? Because I remember both the question and answer. It indeed is 2/3 and I fell for it too, thinking it was 50% at first.

The chance of the second chocolate depends on the first chocolate. So you get P (White|first one white). The chance your first one is white is 1/2 (1/3*1+1/3*0.5+1/3*0). Now if you look at the options left, there are actually 3 and not 2 options. You can first pick the white one and then the black one. You can first pick the left white one and then the right white one. And first right white and then left right. 3 options with an equal chance of happening and 2 of them have 2 whites. So it is 2/3.

5 January 2012, 01:57

Last time edited : 5 January 2012, 01:59

VLLord

Golden Empire

Maybe the following explanation would be easier for understanding. Using conditional probability formula we obtain:

P(second white | first white) = P(both first and second white) / P(first white) = (1/3) / (1/2) = 2/3.

5 January 2012, 12:40

JustNash

Premium Brands

Dutchsmurf
Let me guess, you are Dutch (actually, I know you are) and have been watching tv over the holiday? Because I remember both the question and answer. It indeed is 2/3 and I fell for it too, thinking it was 50% at first.

Nah, I'm Flemish, so please don't insult me like that again Very we!

Just kidding, but yes, I did watch the national science quiz on dutch tv Well

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