Obtain the Probability Distribution of the Random Variable $(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)$

Multiple Choice

Obtain the probability distribution of the random variable.
-When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. $(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)$
$(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)$
$(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)$
$(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)$
$(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)$
$(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)$

Let $X$ denote the smaller of the two numbers. If both dice come up the same number, then $X$ equals that common value. Find the probability distribution of $X$ . Leave your probabilities in fraction form.

A)
$\begin{array}{r|r}x & P(X=x) \\\hline 1 & 5 / 18 \\2 & 1 / 4 \\3 & 7 / 36 \\4 & 5 / 36 \\5 & 1 / 9 \\6 & 1 / 36\end{array}$


B)
$\begin{array}{r|r}\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\\hline 1 & 11 / 36 \\2 & 1 / 4 \\3 & 7 / 36 \\4 & 5 / 36 \\5 & 1 / 12 \\6 & 1 / 36\end{array}$


C)
$\begin{array}{r|r}x & P(X=x) \\\hline 1 & 5 / 18 \\2 & 2 / 9 \\3 & 1 / 6 \\4 & 1 / 9 \\5 & 1 / 18 \\6 & 0\end{array}$

D)
$\begin{array}{r|r}x & P(X=x) \\\hline 1 & 1 / 6 \\2 & 1 / 6 \\3 & 1 / 6 \\4 & 1 / 6 \\5 & 1 / 6 \\6 & 1 / 6\end{array}$