Question

There are two boxes. You have 10 black and 10 white chess pieces. How do you arrange the pieces in the two boxes, so that the probability to pick a white piece is the largest?

Answer 1

Help please :(

Answer 2

does it matter?

Answer 3

Not sure, heh, that's what I am trying to find out

Answer 4

are you picking a box and random, and then picking a piece at random from a box? question is unclear as written

Answer 5

Yes, you pick a box at random and then a piece at random from the box.

Answer 6

I agree that the question was a bit unclear

Answer 7

if you put all white in one box, probability is \(\frac{1}{2}\)
see what happens if you change it, i am willing to bet it makes no difference

Answer 8

That was my thought too, but it seemed a little too easy

Answer 9

for example 5 and 5
probability is \(\frac{1}{2}\times \frac{1}{2}+\frac{1}{2}\times \frac{1}{2}=\frac{1}{2}\)

Answer 10

try it with 3 and 7
i gotta run

Answer 11

\[\frac{1}{2}\times \frac{7}{10}+\frac{1}{2}\times \frac{3}{10}=\frac{1}{2}(\frac{3+7}{10})\] the same

Answer 12

should give an easy proof

Answer 13

Thank you :)

Answer 14

try putting one white piece in a box and all the others in the second box

Answer 15

can you explain the reasoning?

Answer 16

would be very helpful

Answer 17

I got the same answer from another person, but I don't understand it, it seems counterlogical to me

Answer 18

why...the fists box there is a 100% chance of getting a white and the second there is a 9/19 change

so prob of white is

\[\frac{1}{2}\times 1+\frac{1}{2}\frac{9}{19}=\frac{14}{19}\]

Answer 19

which is a lot bigger than 1/2

Answer 20

Thanks

Answer 21

But why is there a 9/19 chance in the second? Sorry, I suck at this

Answer 22

there are only 19 pieces in the second box (one in the first) of those 9 are white

Answer 23

Ohhhhhhh, just realized

Answer 24

I've gone around thinking thinking there had to be 10 in each

Answer 25

Hah, thanks alot :)

Answer 26

would be a boring problem then ;)

Answer 27

Indeed :)

Answer 28

My intuition messed things up for me