We are given $10$ distinct numbers a$1,...,$ a$5$ and b$1,...,$ b$5.$ We know that a$1<$ a$2<$ a$3<$ a$4<$ a$5$ and

b$1<$ b$2<$ b$3<$ b$4<$ b$5.$ Our aim is to find the median of these $10$ numbers $($i$.$e$.,$ the $5-$th smallest$),$ using

as few key comparisons in the worst$-$case as possible.

$$ Draw a decision tree for one such method.

$$ What is the worst$-$case number of comparisons made by your decision tree?