Question 325317
A card is selected from a standard deck of 52 playing cards. Find the probability of selecting 
1. a five given the card is a not a club.
<pre><b>
Since you are given that it is not a club, then you are drawing from a deck of
only 39 cards with no clubs, just hearts, diamonds and spades.  In such a deck,
there are 3 fives.  That's 3 out of 39, so the probability is {{{3/39}}} or
reducing you get {{{1/13}}}.
</pre></b>
 
2. a heart given the card is red.
<pre><b>
Since you are given that it is red, then you are drawing from a deck of only 26
cards with no spades or clubs, just hearts and diamonds.  In such a deck,
there are 2 fives.  That's 2 out of 26, so the probability is {{{2/26}}} or
reducing you get {{{1/13}}}.
</pre></b>

3. a face card, given that the card is black. (An ace is not a face card.) 
<pre><b>
Since you are given that it is black, then you are drawing from a deck of only
26 cards with no hearts or diamonds, just spades and clubs.  In such a deck,
there are 6 face cards, the J,Q and K of spades and the J,Q, and K of clubs. 
That's 6 out of 26, so the probability is {{{6/26}}} or reducing you get
{{{3/13}}}.

Edwin</pre>