if the ball drawn from urn 2 is​ red, what is the probability that the ball drawn from urn 1 was​ red?

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? in decimal form rounded to three decimal places?

Answer 1

For this probability question, the probability of the ball drawn from urn 1 is independent. It does not matter what ball is drawn from urn 2. The probability of drawing any particular ball from urn 1 will stay true to the standard probability formula. It is only the ball drawn from urn 2 that is dependent upon the ball we draw from urn 1. So what is the probability that we draw a red ball from urn 1?

There are 5 red and 5 white balls in urn 1, so the probability of drawing a red ball is

5/10 or 1/2