Probability puzzles




Hard Probability

A soda company is holding a contest where everyone who collects one each of N different coupons wins some prize. You get a coupon with each purchase of a soda, and each coupon is equally likely. What’s the expected number of soda bottles you have to buy in order to collect all the coupons?

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Solution
Source: Quant Interview
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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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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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Answer
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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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