**Instructions:** Use this Conditional Probability calculator to compute the conditional probability \(\Pr(A | B)\). Please provide the probability \(\Pr(A \cap B)\) and \(\Pr(B)\) in the form below:

## Conditional Probability

The concept of conditional probability is one of the most crucial ideas in Probability and Statistics. And it is a quite simple idea: The conditional probability of an event \(A\) *given* an event \(B\) is the probability that \(A\) happens under the assumption that \(B\) happens as well.

This is, we restrict the sample space to outputs in which \(B\) happens, and we look for the probability that \(A\) occurs in that subset sample space.

Now, in mathematical terms, the conditional probability \(\Pr(A|B)\) is computed using the following formula:

\[\Pr(A|B) = \displaystyle \frac{\Pr(A \cap B)}{\Pr(B)}\]The above expression can be rewritten and it also provides a way to compute the probability of the intersection of two event, when the conditional probability is known:

\[ \Pr(A \cap B) = \Pr(A|B) \Pr(B) \]The concept of conditional probability plays a crucial role for the construction of the Total Probability Rule as well as Bayes' Theorem.

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