Instructions: Use this Law of Addition calculator to compute the probability $$\Pr(A \cup B)$$. Please provide the probabilities $$\Pr(A)$$, $$\Pr(B)$$ and $$\Pr(A \cap B)$$ in the form below:

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

## Law of Addition for Computing Probabilities

The Law of Addition is one of the most basic theorems in Probability. It takes a very clear form when depicting it in a Venn-Diagram: The idea is that when we count probabilities for A or B, when we add $$\Pr(A)$$ and $$\Pr(B)$$, it happens that we count twice the portion that corresponds to $$\Pr(A \cap B)$$.

Hence, the Law of Addition takes the following shape:

$\Pr(A \cup B) = \Pr(A) + \Pr(B) - \Pr(A \cap B)$

Notice that re-arranging the above expression, we land into one version of law of multiplication for probabilities.

$\Pr(A \cap B) = \Pr(A) + \Pr(B) - \Pr(A \cup B)$

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