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<b>let </b><font color="Maroon">E</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="rpr_1.html#NM2">Event</a> of <font color="Maroon">E</font>, <font color="Maroon">B</font> be   <a href="rpr_1.html#NM2">Event</a> of <font color="Maroon">E</font>, <font color="Maroon">C</font> be   <a href="rpr_1.html#NM2">Event</a> of <font color="Maroon">E</font>;<br/>



 <a href="rpr_1.html#K1" target="_self">prob</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">C</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <span class="p4">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K9">/\</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p0">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p0">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p5">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E2:34"/>
 <a href="rpr_1.html#K1" target="_self">prob</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p5">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p5">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span></span>)</span>
 ;<br/>


</div>
