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Given a binary search trees for a set of $n=5$ keys with the following probabilities $:$

$\begin{array}{|l|l|l|l|l|l|l|}\hline \text{i} & \text{0} & \text{1}  & \text{2} & \text{3} & \text{4}  & \text{5} \\\hline \text{$p_i$} & \text{-} & \text{0.15}  & \text{0.10} & \text{0.05} & \text{0.10}  & \text{0.20} \\\hline \text{$q_i$} & \text{0.05} & \text{0.10}  & \text{0.05} & \text{0.05} & \text{0.05}  & \text{0.10} \\\hline \end{array}$

The expected optimal cost of the search is

  1. $2.65$
  2. $2.70$
  3. $2.75$
  4. $2.80$
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