There are 6 blue and 5 red marbles in one jar and 5 blue and 4 red marbles in a second jar. If one marble is moved at random from the first jar to the second jar, what is the probability that a blue marble with be pulled from the second jar?

I may be over thinking this or going down the totally wrong direction. I am thinking this is involving Bayes' Rule in some form. I found the probabilities of pulling blue from the second jar given a blue marble was moved and a blue marble was moved and got 5/22 and 18/55 respectively. I then did it for pulling a red marble and got 5/22 and 12/55. Then I took the sum of probabilities for pulling a blue marble and put it over the total possible and got 61/110. I am just afraid I am not taking something into account. Is there a flaw in my logic?