## Probability puzzles

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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Source: Quant Interview
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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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On pressing a button, a random number is generated uniformly between 0 & 1. You keep on generating these numbers until their sum exceeds 1. What is the probability that you need to press the button more than n times? What is the expected number of times you need to press the button?

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You are initially located at origin in the x-axis. You start a random walk with equal probability of moving left or right one step at a time. What is the probability that you will reach point a before reaching point -b? What is the expected number of steps to reach either a or -b? (a,b are natural numbers)

Solution
Source: Top Quant Interview
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You are taking out candies one by one from a jar that has 10 red candies, 20 blue candies, and 30 green candies in it. What is the probability that there are at least 1 blue candy and 1 green candy left in the jar when you have taken out all the red candies? (Candies of same color are indistinguishable!)

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