The Monty
Hall Problem

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Addition and Multiplication Probability Formulas
October 28th, 2016

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Two important probability equations are the multiplication and addition formulas.

The first probability equation is the multiplication formula. This is used to calculate the probability of two events occurring together. The equation is usually written as P(A and B). The formula: P(A and B) = P(A) x P(B). Simple. So the probability of flipping heads and rolling a 4 is 1/2 x 1/6 = 1/12.

The addition formula is used when the question asks about the probability of event A or event B occurring. It’s usually denoted as P(A or B). The probability formula looks like this: P(A or B) = P(A) + P(B) – P(A and B). The probability of flipping heads or rolling a 4 is 1/2 + 1/6 – (1/2 x 1/6) = 7/12.

Basically you add the probability of the two events and then subtract the chance of them both occurring. Picture a venn diagram in which you want to find the total area. To do so, you can find the area of both circles and add them together. But this would double-count the overlapping section of the venn diagram so you need to subtract the area of the overlapping section (in this case, P(A and B)).

There you have it! The two most common probability formulas and equations, the multiplication and addition rules.


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