There are $2$ balls in an urn. Each ball is either white or black. If a white ball is put into an urn and thereafter a ball is drawn at random from the urn, then find the probability that it is white.

Does "each ball is either white or black" mean that there are 3 cases, which are

* $2$ black balls
* $2$ white balls
* $1$ black ball and $1$ white ball?

Also if we add one white ball and then find probability for three cases and then add three probabilities , wouldn't probability be greater than 1?