# Probability theory. I can’t understand why there is information about the second box

#### Imrewq

##### New member
From a box containing 4 white and 6 black balls, one ball is drawn at random and placed in a box containing 5 white and 4 black balls. The ball accidentally taken out of the second box turned out to be black. What is more likely (and by how much): a black ball or a white ball was drawn from the first box?

### Probability theory. I can’t understand why there is information about the second box​

From a box containing 4 white and 6 black balls, one ball is drawn at random and placed in a box containing 5 white and 4 black balls. The ball accidentally taken out of the second box turned out to be black. What is more likely (and by how much): a black ball or a white ball was drawn from the first box?
Because you are to find the probability that the ball from the first box was black, GIVEN that a random ball from the second box is black. The latter does matter.

There are two boxes.
The first box contains 4 white and 6 black balls.
The 2nd box contains 5 white and 4 black balls.

You remove one ball from box 1 and place it into box 2. You then take out a black ball from box 2 (accident or otherwise).
You are asked to determine which is more likely (and by how much): a black ball or a white ball was drawn from the first box?

As Dr Peterson stated, it does matter what was initially in the 2nd box.

It's been a while since the OP posted. Can I answer and then get feedback? I'm not very good at probability.

It's been a while since the OP posted. Can I answer and then get feedback? I'm not very good at probability.
The OP hasn't returned since the day it was posted. Most likely the thread has been abandoned. You're welcome to post your solution for a discussion.

The OP hasn't returned since the day it was posted. Most likely the thread has been abandoned. You're welcome to post your solution for a discussion.
Thanks. First, let me see if my answer is close to what others get.

When a black ball was drawn from the second box, there is a:
34.78% chance that a white ball was drawn from the first box
65.22% chance that a black ball was drawn from the first box

Just for comparison, the first box originally contains 4 white and 6 black, so white should have been drawn 40% of the time, while black should have been drawn 60% of the time.

Thanks. First, let me see if my answer is close to what others get.

When a black ball was drawn from the second box, there is a:
34.78% chance that a white ball was drawn from the first box
65.22% chance that a black ball was drawn from the first box

Just for comparison, the first box originally contains 4 white and 6 black, so white should have been drawn 40% of the time, while black should have been drawn 60% of the time.