Make a Probability Distribution for the Given Set of Events $( 1,1 ) \quad ( 1,2 ) \quad ( 1,3 ) \quad ( 1,4 ) \quad ( 1,5 ) \quad ( 1,6 )$

Make a probability distribution for the given set of events.
-When two fair dice are rolled, 36 equally likely outcomes are possible as shown below. $( 1,1 ) \quad ( 1,2 ) \quad ( 1,3 ) \quad ( 1,4 ) \quad ( 1,5 ) \quad ( 1,6 )$
$( 2,1 ) \quad ( 2,2 ) \quad ( 2,3 ) \quad ( 2,4 ) \quad ( 2,5 ) \quad ( 2,6 )$
$( 3,1 ) \quad ( 3,2 ) \quad ( 3,3 ) \quad ( 3,4 ) \quad ( 3,5 ) \quad ( 3,6 )$
$( 4,1 ) \quad ( 4,2 ) \quad ( 4,3 ) \quad ( 4,4 ) \quad ( 4,5 ) \quad ( 4,6 )$
$( 5,1 ) \quad ( 5,2 ) \quad ( 5,3 ) \quad ( 5,4 ) \quad ( 5,5 ) \quad ( 5,6 )$
$( 6,1 ) \quad ( 6,2 ) \quad ( 6,3 ) \quad( 6,4 ) \quad ( 6,5 ) \quad ( 6,6 )$ Find the probability distribution for the product of the two numbers that appear when two fair dice are rolled.

A)
$\begin{array}{r|r}\text { Product } & \text { Probability } \\\hline 1 & 1 / 18 \\2 & 1 / 18 \\3 & 1 / 18 \\4 & 1 / 18 \\5 & 1 / 18 \\6 & 1 / 18 \\8 & 1 / 18 \\9 & 1 / 18 \\10 & 1 / 18\end{array}$

$\begin{array}{r|r}\text { Product } & \text { Probability } \\\hline 12 & 1 / 18 \\15 & 1 / 18 \\16 & 1 / 18 \\18 & 1 / 18 \\20 & 1 / 18 \\24 & 1 / 18 \\25 & 1 / 18 \\30 & 1 / 18 \\36 & 1 / 18\end{array}$

B)
$\begin{array}{r|r}\text { Product } & \text { Probability } \\\hline 2 & 1 / 36 \\3 & 1 / 18 \\4 & 1 / 12 \\5 & 1 / 9 \\6 & 5 / 36\end{array}$

$\begin{array}{r|r}\text { Product } & \text { Probability } \\\hline 7 & 1 / 6 \\8 & 5 / 36 \\9 & 1 / 9 \\10 & 1 / 12 \\11 & 1 / 18 \\12 & 1 / 36\end{array}$

C)
$\begin{array}{r|r}\text { Product } & \text { Probability } \\\hline 2 & 1 / 18 \\3 & 1 / 18 \\4 & 1 / 12 \\5 & 1 / 18 \\6 & 1 / 9 \\8 & 1 / 18\end{array}$

$\begin{array}{r|r}\text { Product| } & \text { Probability } \\\hline 10 & 1 / 12 \\12 & 1 / 9 \\15 & 1 / 12 \\18 & 1 / 12 \\20 & 1 / 12 \\24 & 1 / 12 \\30 & 1 / 18\end{array}$
D) $$\begin{array}{l}\begin{array} { r | r r | r } \text { Product } & \text { Probability } & \text { Product } & \text { Probability } \\\hline 1 & 1 / 36 & 12 & 1 / 9 \\2 & 1 / 18 & 15 & 1 / 18 \\3 & 1 / 18 & 16 & 1 / 36 \\4 & 1 / 12 & 18 & 1 / 18 \\5 & 1 / 18 & 20 & 1 / 18 \\6 & 1 / 9 & 24 & 1 / 18 \\8 & 1 / 18 & 25 & 1 / 36 \\9 & 1 / 36 & 30 & 1 / 18 \\10 & 1 / 18 & 36 & 1 / 36\end{array}\end{array}$$