Probability
The probability or likelihood of an event is defined as total
number of successes (or frequency of an event occurring)
divided by the sample space (or total number of possible times
for the event to occur.) For example, the probability of rolling
an even number on a standard sixsided die is 3/6 = ½ because
there are six possible outcomes (1,2,3,4,5,6) of which three are
even. It is IMPORTANT to note that each of the outcomes in
the sample space MUST be equally probable for this definition
to be valid. For example, if rolling a 1 was 5 times more likely
than each of a 2, 3, 4, 5, or 6, then ½ would not be the answer
to the question above. We can denote the probability of an
event A occurring as p(A).
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View Full DocumentSome probability rules:
1) The sum of the probabilities of all events/outcomes
occurring is always 1. (Each event/outcome must be
disjoint.)
2) The probability of any event is in between 0 and 1,
inclusive.
3)
If two events A and B are disjoint, then the probability of
either event occurring is the sum of the probability of A
occurring and of B occurring. Symbolically, we have, if
p(A
∩
B) = 0, then p(A
∪
B) = p(A)+p(B).
4) If two events are independent, meaning that one
event does not affect the probability of another
occurring, such as two consecutive flips of a fair
coin, then the probability of both occurring is the
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 Fall '09
 Computer Science, Probability, Probability theory, die roll

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