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Filtered by tag: probability

9 Unfair Coin
Say you have an unfair coin: a coin whose probability of flipping heads and flipping tails is unknown but nonzero. Can you design a game where you and your opponent have an equal chance of winning?
Doable
4.9
9 9 The Monty Hall Problem
You’re on a game show, and you’re given the choice of three doors: Behind one door is a car and behind the other two doors are goats. You pick a door, say No. 1, and the host, who knows what’s behind ...
Doable
5.4
5 6 Lab Rat on the Run
Consider a lab rat in a maze. There are four paths that can be taken with equal probability. Path A leads to exit in 5 minutes. Path B leads back to start and takes 8 minutes. Path C leads to exit in 3 ...
Doable
6.0
4 2 Boys and Girls
To help solve an acute national over-population problem, a government issues a radical decree that families must stop having children as soon as they have had one son. After a while, there are some ...
Doable
5.4
2 3 Death by drawing?
You are a prisoner in a strange foreign land, and a random drawing will decide your fate. You are given 2 bags, 10 white marbles, and 10 black marbles. You are to place the marbles in the bags in any a ...
probability Submitted by Gene
Hard
8.0