Question 208632
Two dice are thrown, the probability that the number on the red exceeds the number showing on the green by exactly two is 
a) 1/18 b) 1/4 c) 1/9 d)1/36 e) 1/24

<pre><font size = 6 color = "indigo">
<b>
Here are all the possible rolls with a 
red die and a green die:
</b>
(<font color="red">1</font>,<font color="green">1</font>) (<font color="red">1</font>,<font color="green">2</font>) (<font color="red">1</font>,<font color="green">3</font>) (<font color="red">1</font>,<font color="green">4</font>) (<font color="red">1</font>,<font color="green">5</font>) (<font color="red">1</font>,<font color="green">6</font>)
 
(<font color="red">2</font>,<font color="green">1</font>) (<font color="red">2</font>,<font color="green">2</font>) (<font color="red">2</font>,<font color="green">3</font>) (<font color="red">2</font>,<font color="green">4</font>) (<font color="red">2</font>,<font color="green">5</font>) (<font color="red">2</font>,<font color="green">6</font>) 

(<font color="red">3</font>,<font color="green">1</font>) (<font color="red">3</font>,<font color="green">2</font>) (<font color="red">3</font>,<font color="green">3</font>) (<font color="red">3</font>,<font color="green">4</font>) (<font color="red">3</font>,<font color="green">5</font>) (<font color="red">3</font>,<font color="green">6</font>)
 
(<font color="red">4</font>,<font color="green">1</font>) (<font color="red">4</font>,<font color="green">2</font>) (<font color="red">4</font>,<font color="green">3</font>) (<font color="red">4</font>,<font color="green">4</font>) (<font color="red">4</font>,<font color="green">5</font>) (<font color="red">4</font>,<font color="green">6</font>)
 
(<font color="red">5</font>,<font color="green">1</font>) (<font color="red">5</font>,<font color="green">2</font>) (<font color="red">5</font>,<font color="green">3</font>) (<font color="red">5</font>,<font color="green">4</font>) (<font color="red">5</font>,<font color="green">5</font>) (<font color="red">5</font>,<font color="green">6</font>)
 
(<font color="red">6</font>,<font color="green">1</font>) (<font color="red">6</font>,<font color="green">2</font>) (<font color="red">6</font>,<font color="green">3</font>) (<font color="red">6</font>,<font color="green">4</font>) (<font color="red">6</font>,<font color="green">5</font>) (<font color="red">6</font>,<font color="green">6</font>) 
<b>
There are 36 possible rolls.  Now I 
will underline just those in which 
the number on the red exceeds the 
number showing on the green by exactly 
two:
</b>
(<font color="red">1</font>,<font color="green">1</font>) (<font color="red">1</font>,<font color="green">2</font>) (<font color="red">1</font>,<font color="green">3</font>) (<font color="red">1</font>,<font color="green">4</font>) (<font color="red">1</font>,<font color="green">5</font>) (<font color="red">1</font>,<font color="green">6</font>)
 
(<font color="red">2</font>,<font color="green">1</font>) (<font color="red">2</font>,<font color="green">2</font>) (<font color="red">2</font>,<font color="green">3</font>) (<font color="red">2</font>,<font color="green">4</font>) (<font color="red">2</font>,<font color="green">5</font>) (<font color="red">2</font>,<font color="green">6</font>) 

<u><b>(<font color="red">3</font>,<font color="green">1</font>)</u></b> (<font color="red">3</font>,<font color="green">2</font>) (<font color="red">3</font>,<font color="green">3</font>) (<font color="red">3</font>,<font color="green">4</font>) (<font color="red">3</font>,<font color="green">5</font>) (<font color="red">3</font>,<font color="green">6</font>)
 
(<font color="red">4</font>,<font color="green">1</font>) <u><b>(<font color="red">4</font>,<font color="green">2</font>)</u></b> (<font color="red">4</font>,<font color="green">3</font>) (<font color="red">4</font>,<font color="green">4</font>) (<font color="red">4</font>,<font color="green">5</font>) (<font color="red">4</font>,<font color="green">6</font>)
 
(<font color="red">5</font>,<font color="green">1</font>) (<font color="red">5</font>,<font color="green">2</font>) <b><u>(<font color="red">5</font>,<font color="green">3</font>)</b></u> (<font color="red">5</font>,<font color="green">4</font>) (<font color="red">5</font>,<font color="green">5</font>) (<font color="red">5</font>,<font color="green">6</font>)
 
(<font color="red">6</font>,<font color="green">1</font>) (<font color="red">6</font>,<font color="green">2</font>) (<font color="red">6</font>,<font color="green">3</font>) <b><u>(<font color="red">6</font>,<font color="green">4</font>)</b></u> (<font color="red">6</font>,<font color="green">5</font>) (<font color="red">6</font>,<font color="green">6</font>)
<b>
There are 36 possible rolls.  So 
there are 4 possible rolls out of
the 36 which have that property.

Therefore the probability is {{{4/36}}} 
which reduces to {{{1/9}}}

Edwin</pre></b></font>









</pre>