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.