A note on independence in probability

We consider here two questions posed by first-year undergraduate students in a statistics tutorial session. These questions are related, and each concerns an aspect of independence in probability. The notion of independence does tend to be a little less intuitive than some of the other elementary probabilistic concepts, thereby providing students with greater opportunities to pose insightful, sophisticated and interesting questions in the classroom or the lecture theatre. With the help of diagrams, we provide solutions to the two questions.