Question 568465
<pre>
Here is a standard deck of 52 cards:

<font color = "red">

A&#9829;   2&#9829;   3&#9829;   4&#9829;   5&#9829;   6&#9829;   7&#9829;   8&#9829;  9&#9829;  10&#9829;  J&#9829;  Q&#9829;  K&#9829; 
A&#9830;   2&#9830;   3&#9830;   4&#9830;   5&#9830;   6&#9830;   7&#9830;   8&#9830;  9&#9830;  10&#9830;  J&#9830;  Q&#9830;  K&#9830;</font>
A&#9824;   2&#9824;   3&#9824;   4&#9824;   5&#9824;   6&#9824;   7&#9824;   8&#9824;  9&#9824;  10&#9824;  J&#9824;  Q&#9824;  K&#9824;</font>  
A&#9827;   2&#9827;   3&#9827;   4&#9827;   5&#9827;   6&#9827;   7&#9827;   8&#9827;  9&#9827;  10&#9827;  J&#9827;  Q&#9827;  K&#9827; 


1. an odd prime number under 10 given the card is a club. (1 is not prime.)

Since we are given that the card is a club, we get rid of all the cards
except the 13 clubs: 

A&#9827;   2&#9827;   3&#9827;   4&#9827;   5&#9827;   6&#9827;   7&#9827;   8&#9827;  9&#9827;  10&#9827;  J&#9827;  Q&#9827;  K&#9827; 

The prime numbers under ten in that group of cards are these four:

     2&#9827;   3&#9827;        5&#9827;        7&#9827;                                 

That's 4 out of 13 or a probability of {{{4/13}}}






2. a Jack, given that the card is not a heart.

Since we are given that the card is a non-heart, we get rid of everything 
but the 39 non-hearts (which is the same as getting rid of the hearts:

<font color = "red">
A&#9830;   2&#9830;   3&#9830;   4&#9830;   5&#9830;   6&#9830;   7&#9830;   8&#9830;  9&#9830;  10&#9830;  J&#9830;  Q&#9830;  K&#9830;</font>
A&#9824;   2&#9824;   3&#9824;   4&#9824;   5&#9824;   6&#9824;   7&#9824;   8&#9824;  9&#9824;  10&#9824;  J&#9824;  Q&#9824;  K&#9824;</font>  
A&#9827;   2&#9827;   3&#9827;   4&#9827;   5&#9827;   6&#9827;   7&#9827;   8&#9827;  9&#9827;  10&#9827;  J&#9827;  Q&#9827;  K&#9827; 

The Jacks in that group are these three:
<font color = "red">
                                                J&#9830;</font>  
                                                J&#9824;
                                                J&#9827;

That's 3 out of 39 or a probability of {{{3/39}}} which reduces to {{{1/13}}}




3.  a King given the card is not a face card.

Since we are given that the card is a non-face card, we get rid of everything 
but the 40 non-face cards (which is the same as getting rid of face cards:

<font color = "red">

A&#9829;   2&#9829;   3&#9829;   4&#9829;   5&#9829;   6&#9829;   7&#9829;   8&#9829;  9&#9829;  10&#9829;   
A&#9830;   2&#9830;   3&#9830;   4&#9830;   5&#9830;   6&#9830;   7&#9830;   8&#9830;  9&#9830;  10&#9830;</font>
A&#9824;   2&#9824;   3&#9824;   4&#9824;   5&#9824;   6&#9824;   7&#9824;   8&#9824;  9&#9824;  10&#9824;</font>  
A&#9827;   2&#9827;   3&#9827;   4&#9827;   5&#9827;   6&#9827;   7&#9827;   8&#9827;  9&#9827;  10&#9827; 

There are 0 Kings in that group, so that's

0 out of 40 or a probability of {{{0/40}}} which reduces to 0

That means that it's impossible, because a King IS a face-card, and if you
are given that it's NOT a face card, then it is impossible to have a King. A
probability of 0 means that it's impossible.  This was a trick question.

Edwin</pre>