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previous outcome and cannot be predicted with certainty.
previous outcome and cannot be predicted with certainty.
Examples
Examples of a Random experiment include:
of a Random experiment include:
The tossing of a coin. The experiment can yield two possible outcomes,
The tossing of a coin. The experiment can yield two possible outcomes,
heads or tails.
heads or tails.
The roll of a die. The experiment can yield six possible outcomes, this
The roll of a die. The experiment can yield six possible outcomes, this
outcome is the number 1 to 6 as the die faces are labelled.
outcome is the number 1 to 6 as the die faces are labelled.
A complete list of all possible outcomes of a random experiment is
A complete list of all possible outcomes of a random experiment is
called '''''sample space''''' or possibility space and is denoted by S
called '''''sample space''''' or possibility space and is denoted by S
In the coin tossing activity S = {heads, tails} and in the dice throwing
activity S = {1,2,3,4,5,6}.
Suppose we toss a coin in the air and note down the result each time. If we
repeat this exercise say 10 times and note down the result each
time. Each toss of a coin is called a '''trial'''.
So, a trial is an action which results in one or several outcomes. The
possible '''outcomes''' when we toss a coin are Head and Tail. Getting a head in a
particular trial is an '''event''' with a particular outcome head.
Now if we say let n be the number of trials, then the '''experimental
probability P(E)''' of an event E happening is given by
[[Image:KOER%20Probability,%20Permutations%20and%20Combinations_html_68e91ef4.gif]]
The probability of E an event happening is always between 0 and 1 including 0 and 1,
where 0 means it is impossible for the event to occur and 1 means its certain to occur.
The
'''theoretical
probability'''
(also called classical probability) of an event E, written as P(E),
where we assume that the outcome of the events are ''equally
likely''
[[Image:KOER%20Probability,%20Permutations%20and%20Combinations_html_48cf88f6.gif]]
In the case of the coin tossing ,
[[Image:KOER%20Probability,%20Permutations%20and%20Combinations_html_m7f38b0db.gif]]
'''Experimental probability'''
The chances of something happening, based on
repeated testing and observing results. It is the ratio of the number
of times an event occurred to the number of times tested. For
example, to find the experimental probability of winning a game, one
must play the game many times, then divide the number of games won by
the total number of games played '''P''''''robability'''
The measure of how likely it is for an event to
occur. The probability of an event is always a number between zero
and 100%. The meaning (interpretation) of probability is the subject
of theories of probability. However, any rule for assigning
probabilities to events has to satisfy the axioms of probability
'''Random number generators'''
A device used to produce a selection of numbers in
a fair manner, in no particular order and with no favour being given
to any numbers. Examples include dice, spinners, coins, and computer
programs designed to randomly pick numbers
'''Theoretical probability'''
The chances of events happening as determined by
calculating results that would occur under ideal circumstances. For
example, the theoretical probability of rolling a 4 on a four-sided
die is 1/4 or 25%, because there is one chance in four to roll a 4,
and under ideal circumstances one out of every four rolls would be a
4. Contrast with experimental probability
= Textbook =
= Textbook =