Finding the probability of picking a blue marble

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?

Re: Finding the probability of picking a blue marble

You are indeed overthinking. The probability of drawing the marble u moved into jar 2 would be 1/10. The probability of picking a blue marble to move would have been 6/11. So the probability of drawing the marble u moved and it being blue is (1/10)(6/11) = 6/110. The probability that a blue marble that was originally in jar 2 was picked up is, 5/10. So 6/110 + 5/10 is the probability of picking a blue marble from jar 2