The stand-in mathematics teacher is forced to choose two students to go on a field trip and he can only choose between the two best girls and the two best boys in the class. He hates the idea of a girl being paired up with a boy, but knows that if he first picks a boy it is much more likely that the next pick will be a girl.

He devises this scheme: He labels 4 otherwise identical tokens with the names of the four students. He puts the tokens into a bag and then reaches in and takes two tokens at exactly the same time, one in each hand.

What is the chance of a boy being paired with a girl with this cunning plan?

The problem was suggested by Leslie Green