Question 96855
<pre>
Two, six sided dice are rolled. Which has the highest probability?
10 ?
9 ?
7 ?
4 ?
2 ? 
<font size = 5><b>
Here are all 36 possible dice rolls:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

--------------------------------------

Now I'll color code them by their sums:

<font color = "magenta">(1,1)</font> (1,2) <font color = "orange">(1,3)</font> (1,4) (1,5) <font color = "green">(1,6)</font> 

(2,1) <font color = "orange">(2,2)</font> (2,3) (2,4) <font color = "green">(2,5)</font> (2,6)

<font color = "orange">(3,1)</font> (3,2) (3,3) <font color = "green">(3,4)</font> (3,5) <font color = "darkblue">(3,6)</font>

(4,1) (4,2) <font color = "green">(4,3)</font> (4,4) <font color = "darkblue">(4,5)</font> <font color = "red">(4,6)</font>

(5,1) <font color = "green">(5,2)</font> (5,3) <font color = "darkblue">(5,4)</font> <font color = "red">(5,5)</font> (5,6)

<font color = "green">(6,1)</font> (6,2) <font color = "darkblue">(6,3)</font> <font color = "red">(6,4)</font> (6,5) (6,6)
<font size = 4>
The 3 <font color = "red">red</font> ones are the 10's, making
     P(10), the probability of rolling a 10, equal to 3/36 

The 4 <font color = "darkblue">blue</font> ones are the 9's, making
     P(9), the probability of rolling a 9, equal to 4/36 

The 6 <font color = "green">green</font> ones are the 7's, making
     P(7), the probability of rolling a 7, equal to 6/36 

The 3 <font color = "orange">yellow</font> ones are the 4's, making
     P(4), the probability of rolling a 4, equal to 3/36 

The <font color = "magenta">pink</font> ones is the only 2, making
     P(2), the probability of rolling a 2, equal to 1/36 

So there are more ways to roll a 7 than there are of rolling any of
the others, so it has the greatest probability, 6/36 which reduces
to 1/6.  So 7 is the correct choice.
<font size = 5>
Edwin</pre>