This is one of the problem from hallelujah1234.

**Quote:**

A box contains 10 white and 5 black balls. 2 balls are taken out at random and put in another nox which was empty. Now a ball is drawn out of this second box at random and it turns out white. What is the probability that the other ball is black.

The link is below.

http://www.gmatclub.com/phpbb/viewtopic.php?t=6000
Let me try to rephrase the problem to see whether I understand it correctly.

OK, so the problem was given that the ball which was drawn out was white. And that is "GIVEN".

So the word which means "GIVEN" tells that the probability is 100%. Is this correct? "GIVEN" means the person who picked out the ball actually saw it as white and picked that particular one. Right?

Let me know if I understand it correctly at this point.

Second question:

What if I change the problem as below which ignore that fact that 2 balls are taken out first, then one was white?

A box contains 10 white and 5 black balls. Someone pulled a white ball out. What is the probability that the person pulls another ball and it is black?
So this problem is similar to the first problem right? Which has the answer 5/14.

Please comment.