How do you calculate theoretical probability?

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Answer 1 · 2014-11-06T11:48:32

Theoretical Probability

Assume that each outcome is equally likely to occur.

Let $S$ be a sample space (the set of all outcomes), and let $E$ be an event (a subset of $S$ ).

The probability of the event $E$ can be found by

$P(E)={n(E)}/{n(S)}$ ,

where $n(E)$ and $n(S)$ denote the number of outcomes in $E$ and the number of outcomes in $S$ , respectively.

Example

What is the probability of rolling a multiple of 3 when you roll a standard die once?

Since all outcomes are 1 through 6, we have the sample space

$S={1,2,3,4,5}$

Since all multiple of 3 are 3 and 6, we have the event

$E={3,6}$

Hence, the probability of rolling a multiple of 3 is

$P(E)={n(E)}/{n(S)}=2/6=1/3$

I hope that this was helpful.