You are presented with three boxes. One of them has a red ball inside and the other two have a black ball inside each of them. You are asked to pick up the one with red ball and you pick one. Now, one of the other boxes is opened and it is found to have a black ball.
You are presented with a chance to change your box with the one that is left closed. Will you change your box? Why or why not?
When you picked up a random box, the probability that the red ball was inside was 1/3.
The chance that red ball was inside one of the two left boxes was 2/3. One box is opened and it is found to have a black ball.
Now you still have a probability of 1/3 that the ball inside your box is red. While the other box has a probability of 2/3 that the red ball is inside since the box that was opened has been taken out.
Thus, you must change the boxes and you will double the chances of getting a red ball.
