<PRE><B>Question 385489</B>
Here is a standard deck of 52 cards:
&lt;pre&gt;
&lt;font color = &quot;red&quot;&gt;
 
A&amp;#9829;   2&amp;#9829;   3&amp;#9829;   4&amp;#9829;   5&amp;#9829;   6&amp;#9829;   7&amp;#9829;   8&amp;#9829;  9&amp;#9829;  10&amp;#9829;  J&amp;#9829;  Q&amp;#9829;  K&amp;#9829; 
A&amp;#9830;   2&amp;#9830;   3&amp;#9830;   4&amp;#9830;   5&amp;#9830;   6&amp;#9830;   7&amp;#9830;   8&amp;#9830;  9&amp;#9830;  10&amp;#9830;  J&amp;#9830;  Q&amp;#9830;  K&amp;#9830;&lt;/font&gt;
A&amp;#9824;   2&amp;#9824;   3&amp;#9824;   4&amp;#9824;   5&amp;#9824;   6&amp;#9824;   7&amp;#9824;   8&amp;#9824;  9&amp;#9824;  10&amp;#9824;  J&amp;#9824;  Q&amp;#9824;  K&amp;#9824;&lt;/font&gt;  
A&amp;#9827;   2&amp;#9827;   3&amp;#9827;   4&amp;#9827;   5&amp;#9827;   6&amp;#9827;   7&amp;#9827;   8&amp;#9827;  9&amp;#9827;  10&amp;#9827;  J&amp;#9827;  Q&amp;#9827;  K&amp;#9827; 

Probability of&lt;/pre&gt; an even number ten or less given the card is a not a diamond.&lt;pre&gt; 

Since we are given that it is not a diamond, we can take out all the diamonds,
and this is what we have left:
&lt;font color = &quot;red&quot;&gt;
A&amp;#9829;   2&amp;#9829;   3&amp;#9829;   4&amp;#9829;   5&amp;#9829;   6&amp;#9829;   7&amp;#9829;   8&amp;#9829;  9&amp;#9829;  10&amp;#9829;  J&amp;#9829;  Q&amp;#9829;  K&amp;#9829; 
&lt;/font&gt;
A&amp;#9824;   2&amp;#9824;   3&amp;#9824;   4&amp;#9824;   5&amp;#9824;   6&amp;#9824;   7&amp;#9824;   8&amp;#9824;  9&amp;#9824;  10&amp;#9824;  J&amp;#9824;  Q&amp;#9824;  K&amp;#9824;&lt;/font&gt;  
A&amp;#9827;   2&amp;#9827;   3&amp;#9827;   4&amp;#9827;   5&amp;#9827;   6&amp;#9827;   7&amp;#9827;   8&amp;#9827;  9&amp;#9827;  10&amp;#9827;  J&amp;#9827;  Q&amp;#9827;  K&amp;#9827;

There are 39 of them.  Now I will underline all the cards that are even number
ten or less: 

&lt;font color = &quot;red&quot;&gt;
A&amp;#9829;   &lt;u&gt;2&amp;#9829;&lt;/u&gt;   3&amp;#9829;   &lt;u&gt;4&amp;#9829;&lt;/u&gt;   5&amp;#9829;   &lt;u&gt;6&amp;#9829;&lt;/u&gt;   7&amp;#9829;   &lt;u&gt;8&amp;#9829;&lt;/u&gt;  9&amp;#9829;  &lt;u&gt;10&amp;#9829;&lt;/u&gt;  J&amp;#9829;  Q&amp;#9829;  K&amp;#9829; 
&lt;/font&gt;
A&amp;#9824;   &lt;u&gt;2&amp;#9824;&lt;/u&gt;   3&amp;#9824;   &lt;u&gt;4&amp;#9824;&lt;/u&gt;   5&amp;#9824;   &lt;u&gt;6&amp;#9824;&lt;/u&gt;   7&amp;#9824;   &lt;u&gt;8&amp;#9824;&lt;/u&gt;  9&amp;#9824;  &lt;u&gt;10&amp;#9824;&lt;/u&gt;  J&amp;#9824;  Q&amp;#9824;  K&amp;#9824;&lt;/font&gt;  
A&amp;#9827;   &lt;u&gt;2&amp;#9827;&lt;/u&gt;   3&amp;#9827;   &lt;u&gt;4&amp;#9827;&lt;/u&gt;   5&amp;#9827;   &lt;u&gt;6&amp;#9827;&lt;/u&gt;   7&amp;#9827;   &lt;u&gt;8&amp;#9827;&lt;/u&gt;  9&amp;#9827;  &lt;u&gt;10&amp;#9827;&lt;/u&gt;  J&amp;#9827;  Q&amp;#9827;  K&amp;#9827;

Count them and you&#39;ll see there are 15 underlined cards, so the
probability is 15 out of 39 or {{{15/39}}} which reduces to {{{5/13}}}

-----------------------------------------------------------------------

As before we start with a standard deck of 52 cards:
&lt;pre&gt;
&lt;font color = &quot;red&quot;&gt;
 
A&amp;#9829;   2&amp;#9829;   3&amp;#9829;   4&amp;#9829;   5&amp;#9829;   6&amp;#9829;   7&amp;#9829;   8&amp;#9829;  9&amp;#9829;  10&amp;#9829;  J&amp;#9829;  Q&amp;#9829;  K&amp;#9829; 
A&amp;#9830;   2&amp;#9830;   3&amp;#9830;   4&amp;#9830;   5&amp;#9830;   6&amp;#9830;   7&amp;#9830;   8&amp;#9830;  9&amp;#9830;  10&amp;#9830;  J&amp;#9830;  Q&amp;#9830;  K&amp;#9830;&lt;/font&gt;
A&amp;#9824;   2&amp;#9824;   3&amp;#9824;   4&amp;#9824;   5&amp;#9824;   6&amp;#9824;   7&amp;#9824;   8&amp;#9824;  9&amp;#9824;  10&amp;#9824;  J&amp;#9824;  Q&amp;#9824;  K&amp;#9824;&lt;/font&gt;  
A&amp;#9827;   2&amp;#9827;   3&amp;#9827;   4&amp;#9827;   5&amp;#9827;   6&amp;#9827;   7&amp;#9827;   8&amp;#9827;  9&amp;#9827;  10&amp;#9827;  J&amp;#9827;  Q&amp;#9827;  K&amp;#9827; 

Probability of &lt;/pre&gt;&lt;/pre&gt;an Ace, given that the card is black.&lt;pre&gt;

Since we are given that the card is black, we will take away all the red ones,
leaving only what is given, the black cards:
 
A&amp;#9824;   2&amp;#9824;   3&amp;#9824;   4&amp;#9824;   5&amp;#9824;   6&amp;#9824;   7&amp;#9824;   8&amp;#9824;  9&amp;#9824;  10&amp;#9824;  J&amp;#9824;  Q&amp;#9824;  K&amp;#9824;&lt;/font&gt;  
A&amp;#9827;   2&amp;#9827;   3&amp;#9827;   4&amp;#9827;   5&amp;#9827;   6&amp;#9827;   7&amp;#9827;   8&amp;#9827;  9&amp;#9827;  10&amp;#9827;  J&amp;#9827;  Q&amp;#9827;  K&amp;#9827; 
 
There are only 26 cards. And only 2 are aces.  So the probability is 2 out
of 26 or {{{2/26}}} wich reduces to {{{1/13}}}

---------------------------------------------------------

As before we start with a standard deck of 52 cards:
&lt;pre&gt;
&lt;font color = &quot;red&quot;&gt;
 
A&amp;#9829;   2&amp;#9829;   3&amp;#9829;   4&amp;#9829;   5&amp;#9829;   6&amp;#9829;   7&amp;#9829;   8&amp;#9829;  9&amp;#9829;  10&amp;#9829;  J&amp;#9829;  Q&amp;#9829;  K&amp;#9829; 
A&amp;#9830;   2&amp;#9830;   3&amp;#9830;   4&amp;#9830;   5&amp;#9830;   6&amp;#9830;   7&amp;#9830;   8&amp;#9830;  9&amp;#9830;  10&amp;#9830;  J&amp;#9830;  Q&amp;#9830;  K&amp;#9830;&lt;/font&gt;
A&amp;#9824;   2&amp;#9824;   3&amp;#9824;   4&amp;#9824;   5&amp;#9824;   6&amp;#9824;   7&amp;#9824;   8&amp;#9824;  9&amp;#9824;  10&amp;#9824;  J&amp;#9824;  Q&amp;#9824;  K&amp;#9824;&lt;/font&gt;  
A&amp;#9827;   2&amp;#9827;   3&amp;#9827;   4&amp;#9827;   5&amp;#9827;   6&amp;#9827;   7&amp;#9827;   8&amp;#9827;  9&amp;#9827;  10&amp;#9827;  J&amp;#9827;  Q&amp;#9827;  K&amp;#9827;

Probability of &lt;/pre&gt;&lt;/pre&gt;a spade given the card is red.&lt;pre&gt;

Since we are given that the card is red, we take away all the black cards,
leaving all the red cards:

&lt;font color = &quot;red&quot;&gt;
 
A&amp;#9829;   2&amp;#9829;   3&amp;#9829;   4&amp;#9829;   5&amp;#9829;   6&amp;#9829;   7&amp;#9829;   8&amp;#9829;  9&amp;#9829;  10&amp;#9829;  J&amp;#9829;  Q&amp;#9829;  K&amp;#9829; 
A&amp;#9830;   2&amp;#9830;   3&amp;#9830;   4&amp;#9830;   5&amp;#9830;   6&amp;#9830;   7&amp;#9830;   8&amp;#9830;  9&amp;#9830;  10&amp;#9830;  J&amp;#9830;  Q&amp;#9830;  K&amp;#9830;&lt;/font&gt;

There are only 26 cards left.

But there are no spades left.  So the probability is 0 out of 26 or {{{0/26}}}
or 0. 

Edwin&lt;/pre&gt;</PRE>