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Probability theory forms the basis for statistics and is reviewed in outline
A probability provides a quantitative description of the likely
occurrence of a particular event. Probability is conventionally expressed
on a scale from 0 to 1; a rare event has a probability close to 0, a very common event
has a probability close to 1.
If S is the set of outcomes of an event all of which are assumed to be equally likely and A is satisfied by a subset A of all of the outcomes.
Then P(A) = N(A) /N(S)
The probability of dealing an Ace from a pack of cards = 4 (number of aces) /52 (total number of cards) = 1/13.Probability Conditions..
The venn diagrams below illustrate various probability conditions.
P(A) ≥ 0 Event A has a probability P(A)
1 ≥ P(E) ≥ 0
For the entire sample space there corresponds the relationship
P(S) = 1
Alternatively .. ∑ i P(A i) = 1 The sum of the probabilities of all possible events A i taking place must be 1.
Example: The entire sample space of tossing a dice S= 1,2,3,4,5,6. The probability P(S)= P(1,2,3,4,5,6) is 1Addition Rule
If events are mutually exclusive P( A ∩ B) = 0 Therefore
For independent events, that is events which have no influence on each other:
It is often required to find the probability of event B if it is known that event A
has taken . This probability is is called the conditional probability if B given A. P(B I A). In this case A serves as the reduced
sample space and the probability is the fraction of P(A) which corresponds to A ∩ B.
example.. A teacher gave his class two tests. 20% of the class passed both tests and 40% of the class passed the first test. What percent of those who passed the first test also passed the second test.
P (Second I First) = P(First and Second) /First = 0,2 /0,4 = 0,5Multiplication Rule
The multiplication rule is a result used to determine the probability that two events, A and B, both occur.
For independent events, that is events which have no influence on each other. This simplifies to:
This results from
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Last Updated 21/09/2007