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* You are guarding 100 murderers in a field, and you have a gun with a single bullet. If any one of the murderers has a non-zero probability of surviving, he will attempt to escape. If a murderer is certain of death, he will not attempt an escape. How do you stop them from escaping?
* One hundred people are in line to board a plane which has exactly 100 seats. Each passenger has a ticket assigning them to a specific seat, and the passengers board one at a time. The first person to board is drunk, picks a random seat, and sits in it. The remaining passengers board; if they find their assigned seat empty, they sit in it. If they find their seat taken, they pick a random seat to sit in. Everyone boards, and is seated. What is the probability that the final person who boards gets to sit in their assigned seat?
* A bag contains N socks, some of which are black, and some of which are red. If two random socks are picked, the probability that they are both red is 1/2. What is the smallest possible value of N for which this is possible?
* You shuffle a standard 52-card deck. What is the probability that the first ace appears exactly at the 20th card?
* For a 3 sets tennis game, would you bet on it finishing in 2 sets or 3 sets?
* I have a square, and place three dots along the 4 edges at random. What is the probability that the dots lie on distinct edges?
* A quantum coin exists in superposition: ǀψ⟩ = αǀH⟩ + βǀT⟩. You can measure it in the {H, T} basis or a rotated {Y, N} basis. Design a protocol to simulate a fair 50/50 coin toss, regardless of α and β. (Assume measurement collapses the state.)
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* You have 17 coins and I have 16 coins, we flip all coins at the same time. If you have more heads then you win, if we have the same number of heads or if you have less then I win. What's your probability of winning?
* What is the probability you draw two cards of the same color from a standard 52-card deck? You are drawing without replacement.
* You're in a room with three light switches, each of which controls one of three light bulbs in the next room. You need to determine which switch controls which bulb. All lights are off to begin, and you can't see into one room from the other. You can inspect the other room only once. How can you find out which switches are connected to which bulbs? Is this possible?
* Find the smallest multi-digit prime number that is a palindrome with an even number of digits.
* Two sentient dice adjust their faces after each roll. If you roll a 4, your die subtracts 1 from its faces; your opponent’s die adds 1. What’s the optimal strategy to maximize the expected sum over three rolls?
* In world series, what are the odds it goes 7 games if each team equal chance of winning?
* If the black hole information paradox resolves in favor of "information loss," you owe $1M; else, you gain $1M. Current physics consensus assigns 70% to "no loss." What’s your expected P&L? How would you hedge this?
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* You’re on a game show with countably infinite doors. Behind one is a car; the rest have goats. After you pick a door, the host (who knows what’s behind all doors) opens all but one other door, revealing goats. Should you switch?
* There is a regular die and a special invisible die. You know that regular die has integers 1 to 6, but don't know what's on the invisible dice. After tossing, I speak the sum of outcome of both die. It so happens that the outcome is an integer between 1 to 12, with equal probability (1/12 each). Can you guess what are the numbers printed on special invisible dice?
* Two witches make a nightly visit to an all-night coffee shop. Each arrives at a random time between 0:00 and 1:00. Each one of them stays for exactly 30 minutes. On any one given night, what is the probability that the witches will meet at the coffee shop?
* In a repeated Prisoner’s Dilemma, what is the Nash equilibrium if both players use tit-for-tat strategies?
* A stick is broken into 3 parts, by choosing 2 points randomly along its length. With what probability can it form a triangle?
* p and q are two points chosen at random between 0 & 1. What is the probability that the ratio p/q lies between 1 & 2?
* A very innocent monkey throws a fair die. The monkey will eat as many bananas as are shown on the die, from 1 to 5. But if the die shows '6', the monkey will eat 5 bananas and throw the die again. This may continue indefinitely. What is the expected number of bananas the monkey will eat?