# Balls in boxes ( probability )

1. Aug 16, 2004

### Rogerio

You have 3 indistinguishable boxes, containing each one, 2 colored balls: black+black, black+white & white+white.

You open one box and, whithout seeing its interior, you take one white ball.

What is the probability of taking a second white ball from the same box?

Last edited: Aug 16, 2004
2. Aug 16, 2004

### Jin314159

Is it 1/2?

And shouldn't this be in the Statistics/Set Theory section?

3. Aug 16, 2004

### Rogerio

No, it's just a brain teaser.
Btw, it seems the correct answer is not 1/2 .

4. Aug 16, 2004

### Jin314159

Oops. I got 1/2 by doing it in my head. When I did it on paper, I got 2/3. Is that right?

5. Aug 16, 2004

### Rogerio

...bingo !

6. Aug 17, 2004

### The Bob

Normally they is an explaination for the stupidier people. WINK WINK

7. Aug 17, 2004

### Rogerio

I would never think of that ! Stupid people doesn't like calculations !

8. Aug 17, 2004

### The Bob

Ok the point is I don't understand and I wish to.

9. Aug 17, 2004

### NateTG

$$\frac{2}{3}$$ seems much too high to me.

Consider, the box that is picked must either be B+W or W+W (since it's impossible to pull B+B). Now, barring some kind of sillyness, that leaves a box containing B or a box containing W. Assuming that the boxes were picked with even probability, that's a 50% probability of getting a white ball.

10. Aug 17, 2004

### Gokul43201

Staff Emeritus
P(A|B)=P(A^B)/P(B)=(1/3)/(1/2) = 2/3

So, what's wrong with the other argument - Nate's ?

Got it - given that the first pick is W, it's twice as likely to be the WW box as it is to be the BW box.

Last edited: Aug 17, 2004
11. Aug 17, 2004

### NateTG

It's unclear what the process is, so the probability could be anything.

The problem doesn't specify that the white ball is chosen at random. If the problem were something like: You pick one ball from the box, what is the probability that the other ball is the same color? The answer would certainly be 2/3.

Last edited: Aug 17, 2004
12. Aug 17, 2004

### BobG

2/3.

There are three white balls you could have pulled out of the box. Of the three, one ball has another black ball in the box. Two balls have another white ball in the box.