A class often students has five males and five females. Five students are selected to give class presentations through the semester. It turns out that only females are selected. The teacher is questioned about this but denies any sex bias.

a. If the teacher selected students entirely at random, how often would it be that only girls were selected for presentation?

b. Do you believe the teacher selected the students at random?

c. The class is divided at random into two tutorial groups of five students. What is the probability that each tutorial group will contain students of one gender? POLI967