Ten students, among them a pair of twins, are divided at random into two teams of five for a quiz. What is the probability that the twins end up on the SAME team?

Follow one twin and ask where the other lands. Once the first twin has been placed, her team has 4 places left and the other team has all 5, so the remaining 9 students fill 4 places beside her and 5 away from her. Every one of those 9 is equally likely to take any place, so the second twin joins her with probability 4/9. The value 1/2 assumes that 'same team or different team' must be an even chance, but the two teams are not symmetric from a twin's point of view — her own team has one seat fewer left in it. The value 5/9 is the complement, the probability that they are separated, and it is indeed the likelier outcome. The value 2/5 = 4/10 counts the 4 free places against all 10 students, forgetting that the first twin has already used one place up.