Maths EE ideas library
Maths Extended Essay ideas: probability
Random walks, paradoxes, games of chance and expected values. Probability EEs can combine exact calculation with simulation to check it.
Probability ideas (10)
- The gambler's ruin problemProbabilitySolid
- Birthday problems beyond birthdaysProbabilityAccessible
- How long to collect the whole set?ProbabilitySolid
- Buffon's needle and estimating πProbabilitySolid
- Monty Hall and its variantsProbabilityAccessible
- Does a random walk come home?ProbabilityAmbitious
- Long-run behaviour of a board gameProbabilitySolid
- Why Benford's law worksProbabilitySolid
- When to stop looking: the secretary problemProbabilityAmbitious
- Penney's game: beating any coin sequenceProbabilitySolid
Frequently asked questions
Is probability a good area for a maths EE?
It can be, if you narrow it to one question you can answer with mathematics you understand. Use simulation to check your exact answer, never as a replacement for it. The analysis is the mathematics; the simulation is evidence.
Can I use one of these research questions as it is?
Use it as a starting point. Change the case, the comparison or the limit until the question is your own, and agree it with your supervisor.
Other areas: Number theory · Algebra · Analysis & calculus · Geometry · Statistics · Modelling · Graph theory · Codes & algorithms · Optimisation & games · History of maths