Let $\mathrm{U}_1$ and $\mathrm{U}_2$ be two urns such that $\mathrm{U}_1$ contains 3 white and 2 red balls, and $\mathrm{U}_2$ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from $\mathrm{U}_1$ and put into $\mathrm{U}_2$. However, if tail appears then 2 balls are drawn at random from $\mathrm{U}_1$ and put into $\mathrm{U}_2$. Now 1 ball is drawn at random from $\mathrm{U}_2$.

Given that the drawn ball from $\mathrm{U}_2$ is white, the probability that head appeared on the coin is