My growing set of problems for the Problem-of-the-Day section of this site now contains a total of 400 problems (each with a worked solution) - 200 SL problems and 200 HL problems. This milestone comes at a time when the launch of the new site for the Analysis & Approaches (SL & HL) is just about to occur. Even with the new site, I will continue to add new problems to the SL PotD and HL PotD lists on this site (until this site closes after the Nov 2020 exams) - but I plan to also start a set of problems on the new Analysis site. My plan is to call this new set of problems the Problem-of-the-Week and for it to be a single list of problems for both SL and HL. I will indicate whether a problem is more suitable for SL or HL students but I'm planning that most of the problems will be suitable for nearly all HL students and for most SL students.  Adding just one problem (and worked solution) each week will give me more time and energy to compose content for the new site. I wish to thank all the teachers who have sent queries and positive feedback for my Problems-of-the-Day.

To mark reaching 400 problems, I would like to offer a nice probability problem that I recently did with my Maths HL students (part (a) below). I don't consider it particularly difficult but it does require some insight - and many students struggle answering it correctly. I also like it because there is an engaging extension to the problem (part (b) below) that asks for a general solution. Here is the problem in two parts with answers viewable below the problem.

probability problem

(a)  A basketball team has 12 players. Alexia and Beatrice are on the team. The players line up randomly in a single straight line for a photograph. What is the probability that Alexia and Beatrice are next to each other?

(b)  There are n people in a group. Charlie and Dexter are in the group. Everyone in the group lines up in randomly in a straight line. What is the probability that Charlie and Dexter are next to each other?