Hudson River Trading–styleSoftware EngineerAlgorithm DeveloperQuestion #14
(1) A 3x3x3 cube has its entire outer surface painted red. After cutting it into 27 unit cubes, one piece is selected at random and placed on a table so that five faces are visible (white). What is the probability that the remaining hidden face is red? (2) Let X be the sum of 100 rolls of a fair six-sided die, and let Y be the number of heads in 600 flips of a fair coin. What is the probability that X is greater than Y, i.e., Pr(X > Y)? (3) Place N points randomly on a circle. What is the probability that all N points lie within a semicircle?
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