Yep, unless I am really misunderstanding the question then there is not enough information here to solve it.
Bayes law say P(A|B) = P(B|A) * P(A)/P(B)
A is Computer science
B is TomLike (i.e. someone with the "description of Tom W")
So P(A|B) is read "the probability of Computer Science given TomLike". In other words this is the chance that someone who is TomLike is in Computer science.
P(B|A) is the probability that someone who is in Computer Science is TomLike. We have to figure out what this is from that strangely worded second part.
P(A) is the chance that someone is in computer science. This is clearly 3%.
P(B) is the chance that someone is TomLike. This is the problem, there is apparently no way to figure this out even if we can what the heck they mean for by that strangly worded phrase for P(B|A).
I don't think this can be solved.