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<div class="headertitle"><div class="title">conditional_probability.cpp File Reference</div></div>
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<p><a href="https://en.wikipedia.org/wiki/Conditional_probability" target="_blank">Conditional Probability</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;stdexcept&gt;</code><br />
<code>#include &lt;string&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for conditional_probability.cpp:</div>
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<p><a href="../../d4/dd1/conditional__probability_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-namespaces" class="groupheader"><a id="namespaces" name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:probability" id="r_probability"><td class="memItemLeft">namespace &#160;</td><td class="memItemRight"><a class="el" href="../../d4/ded/namespaceprobability.html">probability</a></td></tr>
<tr class="memdesc:d4/ded/namespaceprobability"><td class="mdescLeft">&#160;</td><td class="mdescRight">for std::string <br /></td></tr>
<tr class="memitem:conditional_5Fprobability" id="r_conditional_5Fprobability"><td class="memItemLeft">namespace &#160;</td><td class="memItemRight"><a class="el" href="../../df/d4a/namespaceconditional__probability.html">conditional_probability</a></td></tr>
<tr class="memdesc:df/d4a/namespaceconditional__probability"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="https://en.wikipedia.org/wiki/Conditional_probability" target="_blank">Conditional Probability</a> algorithm implementation. <br /></td></tr>
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<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a60e0634bfe8685d623ab52512e84cc9b" id="r_a60e0634bfe8685d623ab52512e84cc9b"><td class="memItemLeft">double&#160;</td><td class="memItemRight"><a class="el" href="#a60e0634bfe8685d623ab52512e84cc9b">probability::conditional_probability::conditional_compute</a> (double p_intersect, double p_given)</td></tr>
<tr class="memdesc:a60e0634bfe8685d623ab52512e84cc9b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the conditional probability P(X|Y). <br /></td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft">static void&#160;</td><td class="memItemRight"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft">int&#160;</td><td class="memItemRight"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
</table>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Conditional_probability" target="_blank">Conditional Probability</a> </p>
<p>In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion, or evidence) is already known to have occurred.</p>
<p>This particular method relies on event A occurring with some sort of relationship with another event B. In this situation, the event A can be analyzed by a conditional probability with respect to B.</p>
<p>If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of
A under the condition B" is given by the formula:</p>
<p class="formulaDsp">
\[P(A \mid B) = \frac{P(A \cap B)}{P(B)}\]
</p>
<p> where: \(P(B) &gt; 0\).</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/SomrajBanik" target="_blank">SomrajBanik</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../d4/dd1/conditional__probability_8cpp_source.html">conditional_probability.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="a60e0634bfe8685d623ab52512e84cc9b" name="a60e0634bfe8685d623ab52512e84cc9b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a60e0634bfe8685d623ab52512e84cc9b">&#9670;&#160;</a></span>conditional_compute()</h2>
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<div class="memproto">
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<td class="memname">double probability::conditional_probability::conditional_compute </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>p_intersect</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>p_given</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
<p>Computes the conditional probability P(X|Y). </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">p_intersect</td><td>probability that both X and Y occur, in [0, P(Y)] </td></tr>
<tr><td class="paramname">p_given</td><td>probability of the event that is given (Y), in (0, 1] </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>P(X|Y) </dd></dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname">std::invalid_argument</td><td>if p_given is not in (0, 1], or if p_intersect is not in [0, p_given] </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="../../d4/dd1/conditional__probability_8cpp_source.html#l00051">51</a> of file <a class="el" href="../../d4/dd1/conditional__probability_8cpp_source.html">conditional_probability.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 51</span> {</div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">if</span> (p_given &lt;= 0.0 || p_given &gt; 1.0) {</div>
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">throw</span> std::invalid_argument(<span class="stringliteral">&quot;The given probability must be in (0, 1].&quot;</span>);</div>
<div class="line"><span class="lineno"> 54</span> }</div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordflow">if</span> (p_intersect &lt; 0.0 || p_intersect &gt; p_given) {</div>
<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">throw</span> std::invalid_argument(</div>
<div class="line"><span class="lineno"> 57</span> <span class="stringliteral">&quot;P(intersection) must be between 0 and the given probability.&quot;</span>);</div>
<div class="line"><span class="lineno"> 58</span> }</div>
<div class="line"><span class="lineno"> 59</span> </div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">return</span> p_intersect / p_given;</div>
<div class="line"><span class="lineno"> 61</span>}</div>
</div><!-- fragment -->
</div>
</div>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d4/dd1/conditional__probability_8cpp_source.html#l00159">159</a> of file <a class="el" href="../../d4/dd1/conditional__probability_8cpp_source.html">conditional_probability.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 159</span> {</div>
<div class="line"><span class="lineno"> 160</span> <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>(); <span class="comment">// run self test implementations</span></div>
<div class="line"><span class="lineno"> 161</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 162</span>}</div>
<div class="ttc" id="acaesar__cipher_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition</b> <a href="../../d6/d2c/caesar__cipher_8cpp_source.html#l00100">caesar_cipher.cpp:100</a></div></div>
</div><!-- fragment -->
</div>
</div>
<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
<div class="memitem">
<div class="memproto">
<table class="mlabels">
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<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">void test </td>
<td>(</td>
<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel static">static</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p>tolerance for double comparison</p>
<p class="definition">Definition at line <a class="el" href="../../d4/dd1/conditional__probability_8cpp_source.html#l00070">70</a> of file <a class="el" href="../../d4/dd1/conditional__probability_8cpp_source.html">conditional_probability.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 70</span> {</div>
<div class="line"><span class="lineno"> 71</span> <span class="keyword">using </span><a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">probability::conditional_probability::conditional_compute</a>;</div>
<div class="line"><span class="lineno"> 72</span> </div>
<div class="line"><span class="lineno"> 73</span> <span class="keyword">const</span> <span class="keywordtype">double</span> epsilon = 1e-9; </div>
<div class="line"><span class="lineno"> 74</span> </div>
<div class="line"><span class="lineno"> 75</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 76</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Testing conditional probability...\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 77</span> </div>
<div class="line"><span class="lineno"> 78</span> <span class="comment">// Test case 1</span></div>
<div class="line"><span class="lineno"> 79</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 1: P(A and B) = 0.2, P(B) = 0.5\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 80</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Expected: P(A|B) = 0.4\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 81</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Result: P(A|B) = &quot;</span> &lt;&lt; <a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(0.2, 0.5) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 82</span> assert(std::fabs(<a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(0.2, 0.5) - 0.4) &lt; epsilon);</div>
<div class="line"><span class="lineno"> 83</span> std::cout &lt;&lt; <span class="stringliteral">&quot;--PASSED--\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 84</span> </div>
<div class="line"><span class="lineno"> 85</span> <span class="comment">// Test case 2</span></div>
<div class="line"><span class="lineno"> 86</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 2: A always happens when B does (B is a subset of A)\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 87</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Expected: P(A|B) = 1.0\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 88</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Result: P(A|B) = &quot;</span> &lt;&lt; <a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(0.5, 0.5) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 89</span> assert(std::fabs(<a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(0.5, 0.5) - 1.0) &lt; epsilon);</div>
<div class="line"><span class="lineno"> 90</span> std::cout &lt;&lt; <span class="stringliteral">&quot;--PASSED--\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 91</span> </div>
<div class="line"><span class="lineno"> 92</span> <span class="comment">// Test case 3</span></div>
<div class="line"><span class="lineno"> 93</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 3: A and B never happen together (mutually exclusive &quot;</span></div>
<div class="line"><span class="lineno"> 94</span> <span class="stringliteral">&quot;events)\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 95</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Expected: P(A|B) = 0.0\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 96</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Result: P(A|B) = &quot;</span> &lt;&lt; <a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(0.0, 0.3) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 97</span> assert(std::fabs(<a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(0.0, 0.3) - 0.0) &lt; epsilon);</div>
<div class="line"><span class="lineno"> 98</span> std::cout &lt;&lt; <span class="stringliteral">&quot;--PASSED--\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 99</span> </div>
<div class="line"><span class="lineno"> 100</span> <span class="comment">// Test case 4</span></div>
<div class="line"><span class="lineno"> 101</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 4: One die, A = &#39;roll is 2&#39;, B = &#39;roll is even&#39;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 102</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Expected: P(A|B) = 1/3 or 0.333333(approx)\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 103</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Result: P(A|B) = &quot;</span></div>
<div class="line"><span class="lineno"> 104</span> &lt;&lt; <a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(1.0 / 6.0, 1.0 / 2.0) &lt;&lt; <span class="stringliteral">&quot; (approx) &quot;</span></div>
<div class="line"><span class="lineno"> 105</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 106</span> assert(std::fabs(<a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(1.0 / 6.0, 1.0 / 2.0) - 1.0 / 3.0) &lt;</div>
<div class="line"><span class="lineno"> 107</span> epsilon);</div>
<div class="line"><span class="lineno"> 108</span> std::cout &lt;&lt; <span class="stringliteral">&quot;--PASSED--\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 109</span> </div>
<div class="line"><span class="lineno"> 110</span> <span class="comment">// Error handling test 1 (Test case 5)</span></div>
<div class="line"><span class="lineno"> 111</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 5: Error handling - P(B) = 0 (invalid)\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 112</span> <span class="keywordtype">bool</span> thrown = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 113</span> <span class="keywordflow">try</span> {</div>
<div class="line"><span class="lineno"> 114</span> <a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(0.2, 0.0);</div>
<div class="line"><span class="lineno"> 115</span> } <span class="keywordflow">catch</span> (<span class="keyword">const</span> std::invalid_argument &amp;e) {</div>
<div class="line"><span class="lineno"> 116</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Error caught: &quot;</span> &lt;&lt; e.what() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 117</span> assert(std::string(e.what()) ==</div>
<div class="line"><span class="lineno"> 118</span> <span class="stringliteral">&quot;The given probability must be in (0, 1].&quot;</span>);</div>
<div class="line"><span class="lineno"> 119</span> thrown = <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 120</span> }</div>
<div class="line"><span class="lineno"> 121</span> assert(thrown);</div>
<div class="line"><span class="lineno"> 122</span> std::cout &lt;&lt; <span class="stringliteral">&quot;--PASSED--\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 123</span> </div>
<div class="line"><span class="lineno"> 124</span> <span class="comment">// Error handling test 2 (Test case 6)</span></div>
<div class="line"><span class="lineno"> 125</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 6: Error handling - P(A and B) &lt; 0 (invalid)\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 126</span> thrown = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 127</span> <span class="keywordflow">try</span> {</div>
<div class="line"><span class="lineno"> 128</span> <a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(-0.1, 0.5);</div>
<div class="line"><span class="lineno"> 129</span> } <span class="keywordflow">catch</span> (<span class="keyword">const</span> std::invalid_argument &amp;e) {</div>
<div class="line"><span class="lineno"> 130</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Error caught: &quot;</span> &lt;&lt; e.what() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 131</span> assert(std::string(e.what()) ==</div>
<div class="line"><span class="lineno"> 132</span> <span class="stringliteral">&quot;P(intersection) must be between 0 and the given probability.&quot;</span>);</div>
<div class="line"><span class="lineno"> 133</span> thrown = <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 134</span> }</div>
<div class="line"><span class="lineno"> 135</span> assert(thrown);</div>
<div class="line"><span class="lineno"> 136</span> std::cout &lt;&lt; <span class="stringliteral">&quot;--PASSED--\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 137</span> </div>
<div class="line"><span class="lineno"> 138</span> <span class="comment">// Error handling test 3 (Test case 7)</span></div>
<div class="line"><span class="lineno"> 139</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 7: Error handling - P(B) &gt; 1 (invalid)\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 140</span> thrown = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 141</span> <span class="keywordflow">try</span> {</div>
<div class="line"><span class="lineno"> 142</span> <a class="code hl_function" href="#a60e0634bfe8685d623ab52512e84cc9b">conditional_compute</a>(0.2, 1.5);</div>
<div class="line"><span class="lineno"> 143</span> } <span class="keywordflow">catch</span> (<span class="keyword">const</span> std::invalid_argument &amp;e) {</div>
<div class="line"><span class="lineno"> 144</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Error caught: &quot;</span> &lt;&lt; e.what() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 145</span> assert(std::string(e.what()) ==</div>
<div class="line"><span class="lineno"> 146</span> <span class="stringliteral">&quot;The given probability must be in (0, 1].&quot;</span>);</div>
<div class="line"><span class="lineno"> 147</span> thrown = <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 148</span> }</div>
<div class="line"><span class="lineno"> 149</span> assert(thrown);</div>
<div class="line"><span class="lineno"> 150</span> std::cout &lt;&lt; <span class="stringliteral">&quot;--PASSED--\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 151</span> </div>
<div class="line"><span class="lineno"> 152</span> std::cout &lt;&lt; <span class="stringliteral">&quot;All tests have successfully passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 153</span>}</div>
<div class="ttc" id="aconditional__probability_8cpp_html_a60e0634bfe8685d623ab52512e84cc9b"><div class="ttname"><a href="#a60e0634bfe8685d623ab52512e84cc9b">probability::conditional_probability::conditional_compute</a></div><div class="ttdeci">double conditional_compute(double p_intersect, double p_given)</div><div class="ttdoc">Computes the conditional probability P(X|Y).</div><div class="ttdef"><b>Definition</b> <a href="../../d4/dd1/conditional__probability_8cpp_source.html#l00051">conditional_probability.cpp:51</a></div></div>
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