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# Conditional Probability

Update your assumptions with the information around you.

Information is at the heart of probability, since a given calculation is only as valid as the assumptions about the situation (and the world around us).

So, how do you adjust probabilities when new information arises? This is where **conditional probability** comes in.

\(P(A\mid B)\) is a conditional probability: "the probability of \(A\) given \(B\)".

\[P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}\]

Intuitively, this formula restricts the sample space to events where \(B\) occurs, and counts events where both \(A\) and \(B\) occur.

By the end of these quizzes, you'll be able to crush the famous Monty Hall Problem, which stumped many mathematicians.

Behind one door is a luxury car, but the other doors contain goats. You choose door #1.

The host will open one of the two doors you didn't choose and will reveal a goat (which he can guarantee, as he knows where the car is). He opens door #3.

Then, you are offered to switch to door #3. Should you?

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