Combinatorics (probability)

Let $U_1$ and $U_2$ be two urns such that $U_1$ contains $3$ white and $2$ red balls, and $U_2$ contains only $1$ ball which is white in colour.A fair coin is tossed.If head appears then $1$ ball is drawn at random from $U_1$ and put into $U_2$ .However, if tail appears then $2$ balls are drawn from $U_1$ and put into $U_2$ .Now $1$ ball is drawn at random from $U_2.$ $\mathbb{\text{What is the probability that the ball is white?.}}$ $\mathbb{\text{The answer is of the form}}$ $\dfrac{p}{q}$ $\mathbb{\text{what is the value of p+q?}}$ $\mathbb{\text{This is a JEE-2011 problem.}}$