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Probability

Counterintuitive odds and chance puzzles

5 RiddlesProbability

The Monty Hall Problem

You're on a game show. Behind one of 3 doors is a car; behind the other two are goats. You pick door 1. The host (who knows what's behind each door) opens door 3 to reveal a goat, then asks if you'd like to switch to door 2. Should you switch?

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mediumAll Ages

The Two-Children Problem

A neighbour says "I have two children, and at least one of them is a boy." What is the probability that both children are boys?

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mediumAll Ages

The Birthday Paradox

How many people do you need in a room before the probability that at least two share a birthday exceeds 50%? (Ignore leap years.)

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easyAll Ages

At Least One Heads

I flip a fair coin twice. You're told that at least one of the flips came up heads. What's the probability that both flips were heads?

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hardAll Ages

Bertrand's Box

Three boxes sit in front of you. Box A has two gold coins, Box B has two silver coins, Box C has one of each. You pick a box at random and draw a coin without looking — it's gold. What's the probability the other coin in that box is also gold?

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