A computer specialty manufacturer has a two-person technical support staff who work independently of each other. In the past, Tom has been able to solve 75% of the problems he has handled, and Adam has been able to solve 95% of the problems he has handled. Incoming problems are randomly assigned to either Tom or Adam.
If a technical problem has just been assigned to the support department, what is the probability that it will be handled by Adam? If it turns out that the problem was solved, what is the probability that it was handled by Adam?