You flip a fair coin until the sequence Tails, Heads, Tails occurs. Your friend flips a different fair coin until the sequence Tails, Heads, Heads occurs. Which of you is expected to flip fewer times in the long run?
You flip a fair coin until the sequence Tails, Heads, Tails or the sequence Tails, Heads, Heads occurs. You win if the sequence is Tails, Heads, Tails, and your friend wins if the sequence is Tails, Heads, Heads. Who is more likely to win?
In a game of Russian roulette, two shots are loaded successively into a six-chambered revolver and the chamber is spun to a random position. You aim the revolver at yourself and pull the trigger, luckily drawing a blank. Now you must take a second shot, but you are given the option of spinning the chamber again before doing so. What should you do?
A 10x10x10 cube is built out of 1x1x1 unit cubes. How many unit cubes are on the surface of the big cube?
Brown eye genes dominate blue eye genes. A person inherits one factor from each parent with equal probability. If both my parents and I have brown eyes and my brother and my wife have blue eyes, what is the probability that my child has blue eyes?
You play a game where a fair coin is flipped and you win $1 if it shows heads and lose $1 if it shows tails. You start with $5 and decide to play until you either have $20 or go broke. What is the probability that you will go broke?
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