finite math question

Question

Urn 1 contains 5 red and 5 white balls. Urn 2 contains 2 red and 7 white balls. A ball is drawn from urn 1 and placed in urn 2. Then a ball is drawn from urn 2. If the ball drawn from urn 2 is​ red, what is the probability that the ball drawn from urn 1 was​ red? round to three decimal places if needed.

Answer 1

Urn 1 contains 5 red and 5 white balls. Therefore, the probability that the red ball is drawn from urn 1 equals to 5/(5 + 5) = 1/2.

Of course, this probability does not depend on the following experiment with urn 2.