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      <text>35.2.2.2 Equi-probable spaces and the principle of equally likely outcomes</text>
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      <text><![CDATA[<h4> Equi-probable spaces and the principle of equally likely outcomes </h4>
<p>An equi-probable space is a sample space in which the chance that any one sample point occurs is equal to the chance that any other sample point occurs. Whether a sample space is an equi-probable space is usually determined by inspection or logic.</p><p>
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<li> Tossing a coin. The sample space \(S\) is, using an obvious notation\[S = \{H,T\}\]\(H\) and \(T\) are the two simple outcomes and are equally likely to occur.</li>
<li> Rolling a 6-faced die. A sample space is:\[S = \{1,2,3,4,5,6\}\]Each number from \(1\) to \(6\) is a simple outcome and is equally likely to occur.</li>
<li> Tossing three coins. A sample space comprised of simple outcomes is:\[S = \{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\}\]Each of the eight outcomes stated is equally likely to occur.</li>
<li> Counting the number of heads when three coins are tossed. Here\[S = \{3\text{ Heads},2\text{ Heads},1\text{ Head},0\text{ Heads}\}.\]This is not an equi-probable space and the outcomes are not equally likely. (For example: the event \(\{2\text{ Heads}\}\) is the union of three simple events
\(\{HHT,HTH,THH\}\) so must occur more often than the event \(\{HHH\}\).</li>
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<p>Of the sample spaces above all are equi-probable spaces except for (d).</p>
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<h4> Key Point </h4>
<h5> The Principle of Equally Likely Outcomes </h5>
<p>This states that each simple outcome in an equi-probable space is equally likely to occur. This
principle enables us to deduce the probabilities that simple events (and hence more complicated
events which are combinations of simple events) occur.</p>
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