Consider a binary search tree whose nodes correspond to the seven MnSCU state universities.

Students search for information about these universities, and their queries about given universities are routed to th BST$.$

Asume that no student ever searches for a non$-$existent university $($there$\text{'}$s a group of radio buttons or something to keep them from screwing up$).$

The probabilities of students searching for the various universities are given in the following table:

The binary search tree is set up as a balanced tree, as in the figure.

To the nearest $10$ th$,$ what is the mean number of queries made per search?

$1)2\mathrm{.}3$

$2)2\mathrm{.}4$

$3)2\mathrm{.}5$

$4)2\mathrm{.}6$