Lauretta J. Fox
To perform experiments scientists must select individuals or samples from a population. A random sample is one in which each member of the population has an equal chance of being selected. If selections favor certain individuals or events the sampling is said to be biased. The result of each experiment is called an event or outcome, and the set of all possible outcomes is known as a sample space.
Example 1:
Each positive integer from one to five inclusive is written on a piece of paper, and the pieces of paper are shuffled. List a sample space for the outcome of drawing one piece of paper.
Solution:
Any one of the five numbers is equally likely to be drawn. The sample space is (1,2,3,4,5).
Example 2:
Two jelly beans are to be drawn from a jar known to contain only red jelly beans and green jelly beans. List a sample space for the result of the drawing.
Solution:
Since the jelly beans must be red or green, a sample space is
{ (R,G), (R,R), (G,R), (G,G)}
Exercises
Complete each statement in exercises 1—4.
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1.) A ___ ___ is a sample in which each member of a population is equally likely to be selected.
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2.) A sample is ___ when certain individuals are favored in a selection.
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3.) The result of an experiment is called an ___ or an ___
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4.) The set of all possible outcomes is known as a ___.
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5.) Each letter in the word flower is written on a card and the cards are shuffled. List a sample space for the outcome of drawing one card.
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6.) Two balls are to be drawn successively from a bag known to contain only yellow balls and purple balls. List a sample space for the experiment.
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7.) List a sample space that indicates all possible outcomes when two dice are thrown.
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8.) List a sample space to show all possible outcomes when a family has three children.
