 # Conditional Probability Calculator

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: Please indicate the value of $$\Pr(A \cap B)$$ = Please indicate the value of $$\Pr(B)$$ =

## 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 wel as Bayes' Theorem.

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