Hard puzzles




Hard Probability

You have 100 noodles in your soup bowl. You are told to take two ends of some noodles (each end on any noodle has the same probability of being chosen) in your bowl and connect them. You continue until there are no free ends. What is the expected number of loops? What is the probability of making one large loop which includes every noodle?

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Hard Probability

Given the set of numbers from 1 to n: { 1, 2, 3 .. n } We draw n numbers randomly (with uniform distribution) from this set (with replacement). What is the expected number of distinct values that we would draw?

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Answer
Solution
Source: CSEblog
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Hard Probability

What is the expected number of cards that need to be turned over in a regular 52-card deck in order to see the first ace?

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Hard Probability

x & y are two random points selected uniformly between 0 & 1. Using them, create a point uniformly random in circle of radius 1. (uniform means that the probability density is constant)

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Solution
Source: Quant Interview
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Hard Probability

N points are chosen at random on the cicumference of a circle. A convex n-gon (n sided polygon) is drawn by joining these n points. What is the probability that the center of circle lies inside the region of n-gon?

Solution
Source: a nice senior
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