X_1, X_2, ..., X_N are N random variables drawn from Uniform distribution on [0, 1]. What is the probability of the average of X is greater than 1?
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You are given 2 eggs. * You have access to a 100-storey building. * Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100 th floor.Both eggs are identical. * You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking. * Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process
Let a rope of unit length is cut into n pieces. What is the expected length of the smallest piece?
You are playing a game and the probability of winning is 0.6. Would you rather play best of 3, or play until someone is ahead by 2 points?
V~U[0,1]. Make a bet B, for V, and will be awarded 1,5 times V if B>V, otherwise your bet is worthless - you do not lose anything as well. What is your bet?
Robot wakes up every morning and does one of the following things with equal (1/4) probability: 1) self-destroys; 2) does nothing; 3) clones himself (so you have 2 robots); 4) clones himself two times (so you have 3 robots). If you have one robot at the start of the first day, what is the probability that, eventually, you will have no robots?
Given four uniform variables iid on [0,1], we connect the first two and connect the last two to form line segments. What is the probability that these segments overlap?
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