Cute problem. And you can probably go a bit further in assessing how good your best guess is by inferring that the class size is at least 20 and lower bounding your variances.
[Or you can be dickish/clever and claim that the problem is underspecified because you're only given the overall boy/girl percentages for the two programs, and not their distribution. E.g., if each class has either exactly 65% or exactly 45% boys, then your observation is consistent with neither of the classes.]
[Actually you can't be dickish/clever that way: The problem isn't underspecified as the goal is to do the best you can with the information you've got. You've got no information/evidence regarding the distribution between classes so your best bet is to treat it as random. From there you can use Bayes theorem, blah blah, etc. etc....]
Found in an old Kahneman & Tversky paper: