$010$ observations in two classes $($black and red$)$ are given according to the table.

$\backslash$table$[[,$o$\_(1),$o$\_(2),$o$\_(3),$o$\_(4),$o$\_(5),$o$\_(6),$o$\_(7),$o$\_(8),$o$\_(9),$o$\_(10)],[$o$\_(1),0\mathrm{.}0,1\mathrm{.}3,4\mathrm{.}1,3\mathrm{.}8,4\mathrm{.}5,2\mathrm{.}4,3\mathrm{.}2,2\mathrm{.}7,3\mathrm{.}0,3\mathrm{.}9],[$o$\_(2),1\mathrm{.}3,0\mathrm{.}0,3\mathrm{.}2,3\mathrm{.}1,4\mathrm{.}7,2\mathrm{.}3,2\mathrm{.}6,2\mathrm{.}2,2\mathrm{.}7,4\mathrm{.}2],[$o$\_(3),4\mathrm{.}1,3\mathrm{.}2,0\mathrm{.}0,0\mathrm{.}4,4\mathrm{.}9,2\mathrm{.}7,1\mathrm{.}1,1\mathrm{.}6,2\mathrm{.}4,4\mathrm{.}8],[$o$\_(4),3\mathrm{.}8,3\mathrm{.}1,0\mathrm{.}4,0\mathrm{.}0,4\mathrm{.}6,2\mathrm{.}5,0\mathrm{.}9,1\mathrm{.}3,2\mathrm{.}1,4\mathrm{.}5],[$o$\_(5),4\mathrm{.}5,4\mathrm{.}7,4\mathrm{.}9,4\mathrm{.}6,0\mathrm{.}0,3\mathrm{.}1,4\mathrm{.}4,3\mathrm{.}7,2\mathrm{.}8,2\mathrm{.}3],[$o$\_(6),2\mathrm{.}4,2\mathrm{.}3,2\mathrm{.}7,2\mathrm{.}5,3\mathrm{.}1,0\mathrm{.}0,1\mathrm{.}8,1\mathrm{.}2,0\mathrm{.}9,2\mathrm{.}8],[$o$\_(7),3\mathrm{.}2,2\mathrm{.}6,1\mathrm{.}1,0\mathrm{.}9,4\mathrm{.}4,1\mathrm{.}8,0\mathrm{.}0,1\mathrm{.}0,1\mathrm{.}7,4\mathrm{.}1],[$o$\_(8),2\mathrm{.}7,2\mathrm{.}2,1\mathrm{.}6,1\mathrm{.}3,3\mathrm{.}7,1\mathrm{.}2,1\mathrm{.}0,0\mathrm{.}0,1\mathrm{.}1,3\mathrm{.}6],[$o$\_(9),3\mathrm{.}0,2\mathrm{.}7,2\mathrm{.}4,2\mathrm{.}1,2\mathrm{.}8,0\mathrm{.}9,1\mathrm{.}7,1\mathrm{.}1,0\mathrm{.}0,2\mathrm{.}9],[$o$\_(10),3\mathrm{.}9,4\mathrm{.}2,4\mathrm{.}8,4\mathrm{.}5,2\mathrm{.}3,2\mathrm{.}8,4\mathrm{.}1,3\mathrm{.}6,2\mathrm{.}9,0\mathrm{.}0]]$

Consider the dendrogram shown with $3$ clusters which is based on the observations and distances

in the Table using single linkage.

Suppose we apply a cutoff $($indicated by the black

line$)$ thereby generating three clusters. We

wish to compare the quality of this clustering, Q$,$ to the

ground$-$truth clustering, Z$,$ indicated by the colors in

Table $2.$ What is the Rand index of the two clusterings?