5.1 Probabilities
In every day experience, terms such as almost certain or quite
unlikely
are often used.
In science however we must be more precise
in the terms. We would also like to be able to quantify statements.
The quantification of the degree of certainty is the area of study
called
probability.
You are already familiar with some probability. Since coin has 2
sides
we say that the probability of getting heads on the flip of a
fair coin is 0.5.
Therefore, the probability of an event can be
defined as the fraction of the total number of outcomes that will
result in the event. More formally this concept can be defined as:
Classical Definition of Probability
If there are n equally likely outcomes of an experiment and an event
E consists of s of these outcomes then the probability of E is s/n.
For example, there are 52 cards in a deck,
including 4 aces, thus we
say the probability of drawing an ace from a deck is 4/52.
Likewise,
the probability of getting an even number of dots showing when we
throw a fair die = 3/6 = 1/2.
Frequency (Empirical) Definition of Probability
Returning to the coin example, when we state that a fair coin will come
up heads half the time we are saying that the probability of heads =
0.5.
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 Fall '10
 RaySievers
 Statistics, Probability, Probability theory, Coin flipping, exclusive or

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