Consider the experiment where a pair of fair dice is thrown.

Let $X$ denote the random variable whose value is determined by taking the maximum of the spots showing on either of the two dice thrown. For example, if a 3 and a 5 were thrown, then $X$ would take the value of $\mbox{max}(3,5) = 5$. Note that the range of values that $X$ can assume are the positive integers $\lbrace 1,2,3,4,5,6\rbrace$.

Find each of the probabilities below (note that this specifies the PDF for $X$).

$Pr(X = 1) =$
$Pr(X = 2) =$
$Pr(X = 3) =$
$Pr(X = 4) =$
$Pr(X = 5) =$
$Pr(X = 6) =$

Further, find the probability that $X$ is divisible by $3$:
$Pr(X \mbox{ is divisible by } 3) =$