Question 427342
1. A card is drawn from an ordinary deck and we are told that it is red, what is the probability that the card is greater than 2 but less than 9?

<pre><font face = "consolas" size = 4><b>

Here is a complete 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;  
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; 
 
We are told that the card is red, so we can remove all the 
black cards and have only this smaller deck of 26 red 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>
 
<pre><font face = "consolas" size = 4><b>
So we want the probabilty that out of those 26 red cards, 
the card that is drawn is one of these 12:

<font color = "red">
          3&#9829;   4&#9829;   5&#9829;   6&#9829;   7&#9829;   8&#9829;   
          3&#9830;   4&#9830;   5&#9830;   6&#9830;   7&#9830;   8&#9830;</font>
 
<pre><b>
So the desired probability is 12 out of 26, or 12/26 
which reduces to 6/13.

Edwin</pre>