Geometric Probability and Order Statistics
Screening interviews often move from dice and cards to continuous questions: two people arriving at random times, a stick broken at random points, the best of several random bids. These look harder than discrete problems, but most reduce to one of two tools. When the random quantities are uniform, a probability is an area. When the question is about the largest or smallest of several draws, it is an order statistic, and a short formula gives the answer.
Probability as area
When points are chosen uniformly in a region, the probability of an event is the area of the part of the region where it happens, divided by the total area. The method is always the same: draw the space of outcomes, shade the event, and compute the shaded area, often through its complement.
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