I sample p uniformly from [0,1] and flip a coin 100 times. The coin lands heads with probability p in each flip. Before each flip, you are allowed to guess which side it will land on. For each correct guess, you gain 1$, for each incorrect guess you lose 1$. What would your strategy be and would you pay 20$ to play this game?
Three games, you need to decide which one to play: 1) Throw a normal dice and take the square of the resulting value 2) Throw two dice and take the product of the results 3) Throw 5 dice and take the square of the mode.
Mostly based on basic ideas about probabilities, but quite hard to grasp unless you have the right intuition. One example: estimate probability of a certain outcome in a heads/tails game
Statistics and probability problems and questions
Probability question
Questions about probability theory, data structures, etc. I studied some quantitative finance, but they did not ask me about that.
Brain teasers
What is the expected value of a die roll?
Probability based questions e.g. coin tossing, Markov chain (without mentioning the concept directly)
Various mock trading scenarios which make use of the ideas in the Probability and Markets Guide on their website (expected value, adverse selection etc).
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