# OpenDocProject:Stats400/2010/08/25

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## Notes Lecture 2

Probability: any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions.

##### Probability Theory

The outcome of a random phenomenon (such as having a heart attack or being in a car accident) is unpredictable. However, in a very long series of independe~t repetition~ a stable attern emerges that can be described in terms of observed relative frequencIes of the vanous possIble outcomes.

Consider a particular outcome. We are interested in the theoretical probability of the outcome:

P(outcome) = fraction of times the outcome would occur in an infinitely long series of independent repetitions.

To estimate (guess) the probability we consider a number of independent repetitions and compute the experimental probability,

P(outcome) = number of successful repetitions

```                        total number of repetitions
```

= relative frequency of the outcome.