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# Brain-Warping Probability

Most people's intuitions about the odds of winning these games are wrong.

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Probabilities can be tricky, and these quizzes explore some brain-warping problems where the answer is not what it might seem at first. You'll use conditional probability and Bayes' theorem to tackle famous problems like the Monty Hall problem and the boy-girl paradox.

A family has two children and gives the hint that "at least one of them is a girl born on a Tuesday." What is the probability that both children are girls?

The first quiz will work through a famous gambling problem inspired by the game show "Let’s Make a Deal", which was popular in the 1960s and 1970s. You are a contestant on a game show. Here are the rules of the game show:

• There are 3 doors, and Monty Hall, the host of the game show, has made sure that there's a car behind one of these 3 doors, and man-eating goats behind the other two doors.

• At the start of the game, you may choose any one of the three doors.

• After you pick one of the 3 doors, Monty Hall opens one of the two doors that you did not pick, and shows you that there is a goat behind that door. (Monty Hall is not allowed to open your door, and he knows where the car is and will not open a door if the car is behind that door.)

• Finally, Monty Hall asks you if you want to switch doors. In other words, you can either choose to stay with the door that you initially chose, or switch to the other door that’s still unopened.

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